Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,19 +0,0 @@
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generic
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type Result_Type (<>) is limited private;
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None: Result_Type;
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with function One(X: Positive) return Result_Type;
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with function Add(X, Y: Result_Type) return Result_Type
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is <>;
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package Generic_Divisors is
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function Process
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(N: Positive; First: Positive := 1) return Result_Type is
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(if First**2 > N or First = N then None
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elsif (N mod First)=0 then
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(if First = 1 or First*First = N
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then Add(One(First), Process(N, First+1))
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else Add(One(First),
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Add(One((N/First)), Process(N, First+1))))
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else Process(N, First+1));
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end Generic_Divisors;
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@ -1,59 +0,0 @@
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with Ada.Text_IO, Ada.Containers.Generic_Array_Sort, Generic_Divisors;
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procedure Proper_Divisors is
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begin
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-- show the proper divisors of the numbers 1 to 10 inclusive.
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declare
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type Pos_Arr is array(Positive range <>) of Positive;
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subtype Single_Pos_Arr is Pos_Arr(1 .. 1);
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Empty: Pos_Arr(1 .. 0);
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function Arr(P: Positive) return Single_Pos_Arr is ((others => P));
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package Divisor_List is new Generic_Divisors
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(Result_Type => Pos_Arr, None => Empty, One => Arr, Add => "&");
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procedure Sort is new Ada.Containers.Generic_Array_Sort
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(Positive, Positive, Pos_Arr);
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begin
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for I in 1 .. 10 loop
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declare
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List: Pos_Arr := Divisor_List.Process(I);
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begin
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Ada.Text_IO.Put
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(Positive'Image(I) & " has" &
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Natural'Image(List'Length) & " proper divisors:");
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Sort(List);
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for Item of List loop
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Ada.Text_IO.Put(Positive'Image(Item));
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end loop;
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Ada.Text_IO.New_Line;
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end;
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end loop;
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end;
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-- find a number 1 .. 20,000 with the most proper divisors
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declare
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Number: Positive := 1;
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Number_Count: Natural := 0;
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Current_Count: Natural;
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function Cnt(P: Positive) return Positive is (1);
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package Divisor_Count is new Generic_Divisors
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(Result_Type => Natural, None => 0, One => Cnt, Add => "+");
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begin
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for Current in 1 .. 20_000 loop
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Current_Count := Divisor_Count.Process(Current);
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if Current_Count > Number_Count then
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Number := Current;
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Number_Count := Current_Count;
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end if;
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end loop;
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Ada.Text_IO.Put_Line
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(Positive'Image(Number) & " has the maximum number of" &
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Natural'Image(Number_Count) & " proper divisors.");
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end;
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end Proper_Divisors;
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@ -1,33 +1,31 @@
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-->
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<span style="color: #008080;">global</span> <span style="color: #008080;">function</span> <span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">include1</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #000080;font-style:italic;">--
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-- returns a list of all integer factors of n
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-- if include1 is 0 (the default), result does not contain either 1 or n
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-- if include1 is 1 the result contains 1 and n
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-- if include1 is -1 the result contains 1 but not n
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-- </span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">check_limits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"factors"</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">lfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span> <span style="color: #000000;">hfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">hfactor</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span>
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<span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
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global function factors(atom n, integer include1=0)
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--
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-- returns a list of all integer factors of n
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-- if include1 is 0 (the default), result does not contain either 1 or n
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-- if include1 is 1 the result contains 1 and n
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-- if include1 is -1 the result contains 1 but not n
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--
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if n=0 then return {} end if
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check_limits(n,"factors")
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sequence lfactors = {}, hfactors = {}
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atom hfactor
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integer p = 2,
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lim = floor(sqrt(n))
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<span style="color: #008080;">if</span> <span style="color: #000000;">include1</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">lfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">include1</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">hfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">}</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">p</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">lim</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">lfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lfactors</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">hfactor</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">p</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">hfactor</span><span style="color: #0000FF;">=</span><span style="color: #000000;">p</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">hfactors</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hfactors</span><span style="color: #0000FF;">,</span><span style="color: #000000;">hfactor</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">p</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">lfactors</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">hfactors</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<!--
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if include1!=0 then
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lfactors = {1}
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if n!=1 and include1=1 then
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hfactors = {n}
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end if
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end if
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while p<=lim do
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if remainder(n,p)=0 then
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lfactors = append(lfactors,p)
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hfactor = n/p
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if hfactor=p then exit end if
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hfactors = prepend(hfactors,hfactor)
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end if
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p += 1
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end while
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return lfactors & hfactors
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end function
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@ -1,20 +1,18 @@
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(phixonline)-->
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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for i=0 to 10 do
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printf(1,"%d: %v\n",{i,factors(i,-1)})
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end for
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">maxd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20000</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">maxd</span> <span style="color: #008080;">then</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">maxd</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">else</span>
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<span style="color: #000000;">candidates</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">}</span>
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<span style="color: #000000;">maxd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d divisors: %v\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">maxd</span><span style="color: #0000FF;">,</span><span style="color: #000000;">candidates</span><span style="color: #0000FF;">})</span>
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<!--
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sequence candidates = {}
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integer maxd = 0
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for i=1 to 20000 do
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integer k = length(factors(i,-1))
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if k>=maxd then
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if k=maxd then
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candidates &= i
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else
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candidates = {i}
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maxd = k
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end if
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end if
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end for
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printf(1,"%d divisors: %v\n", {maxd,candidates})
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@ -1,17 +0,0 @@
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function proper-divisor ($n) {
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if($n -ge 2) {
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$lim = [Math]::Floor([Math]::Sqrt($n))
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$less, $greater = @(1), @()
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for($i = 2; $i -lt $lim; $i++){
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if($n%$i -eq 0) {
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$less += @($i)
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$greater = @($n/$i) + $greater
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}
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}
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if(($lim -ne 1) -and ($n%$lim -eq 0)) {$less += @($lim)}
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$($less + $greater)
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} else {@()}
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}
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"$(proper-divisor 100)"
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"$(proper-divisor 496)"
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"$(proper-divisor 2048)"
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@ -1,15 +0,0 @@
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function proper-divisor ($n) {
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if($n -ge 2) {
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$lim = [Math]::Floor($n/2)+1
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$proper = @(1)
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for($i = 2; $i -lt $lim; $i++){
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if($n%$i -eq 0) {
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$proper += @($i)
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}
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}
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$proper
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} else {@()}
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}
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"$(proper-divisor 100)"
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"$(proper-divisor 496)"
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"$(proper-divisor 2048)"
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@ -1,49 +0,0 @@
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function eratosthenes ($n) {
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if($n -gt 1){
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$prime = @(0..$n| foreach{$true})
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$m = [Math]::Floor([Math]::Sqrt($n))
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function multiple($i) {
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for($j = $i*$i; $j -le $n; $j += $i) {
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$prime[$j] = $false
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}
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}
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multiple 2
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for($i = 3; $i -le $m; $i += 2) {
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if($prime[$i]) {multiple $i}
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}
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2
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for($i = 3; $i -le $n; $i += 2) {
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if($prime[$i]) {$i}
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}
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} else {
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Write-Error "$n is not greater than 1"
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}
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}
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function prime-decomposition ($n) {
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$array = eratosthenes $n
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$prime = @()
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foreach($p in $array) {
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while($n%$p -eq 0) {
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$n /= $p
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$prime += @($p)
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}
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}
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$prime
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}
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function proper-divisor ($n) {
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if($n -ge 2) {
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$array = prime-decomposition $n
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$lim = $array.Count
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function state($res, $i){
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if($i -lt $lim) {
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state ($res) ($i + 1)
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state ($res*$array[$i]) ($i + 1)
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} elseif($res -lt $n) {$res}
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}
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state 1 0 | sort -Unique
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} else {@()}
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}
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"$(proper-divisor 100)"
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"$(proper-divisor 496)"
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"$(proper-divisor 2048)"
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@ -1,5 +1,5 @@
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-- 8 May 2025
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include Settings
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-- 24 Aug 2025
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include Setting
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numeric digits 30
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call Time('r')
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@ -56,7 +56,4 @@ end
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say
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return
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include Sequences
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include Functions
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include Special
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include Abend
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include Math
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@ -1,5 +1,5 @@
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ADx ← |1 ⨬(◴⊂⊂⊃(⊙∘|/⊂⊞×)\×°□⊙ADx°⊂|[1])=0⧻.
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ADs ← ⊏⊸⍏ADx⊕□⊸⊛°/× # All divisors including 1, n.
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ADx ← |1 ⨬(◴⊂⊂⊃(⊙∘|/⊂⊞×)\×°□⊙ADx°⊂|[1])=0⊸⧻
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ADs ← ⍆ADx⊕□⊸⊛°/× # All divisors including 1, n.
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PDs ← ↘¯1ADs # Proper Divisors.
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≡(□PDs)+1⇡10 # Proper Divisors of 1 to 10.
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⟜(▽=)/↥.≡(⧻PDs).+1⇡2e4 # Numbers below 20k with most PDs.
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⟜(▽=)⊸/↥⊸≡(⧻PDs)+1⇡2e4 # Numbers below 20k with most PDs.
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