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12390 changed files with 318560 additions and 27248 deletions
37
Task/Tau-function/ALGOL-60/tau-function.alg
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37
Task/Tau-function/ALGOL-60/tau-function.alg
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@ -0,0 +1,37 @@
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begin
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comment - return n mod m;
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integer procedure mod(n, m);
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value n, m; integer n, m;
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begin
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mod := n - entier(n/m) * m;
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end;
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comment - return number of divisors of n;
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integer procedure tau(n);
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value n; integer n;
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begin
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integer i, t, limit;
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if n < 3 then
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t := n
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else
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begin
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t := 2;
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limit := (n + 1) / 2;
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for i := 2 step 1 until limit do
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begin
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if mod(n, i) = 0 then t := t + 1;
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end;
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end;
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tau := t;
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end;
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integer i;
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outstring(1,"Number of divisors of first 100 numbers\n");
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for i := 1 step 1 until 100 do
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begin
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outinteger(1,tau(i));
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if mod(i,10) = 0 then outstring(1,"\n");
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end;
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end
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23
Task/Tau-function/Agena/tau-function.agena
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23
Task/Tau-function/Agena/tau-function.agena
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@ -0,0 +1,23 @@
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scope # find the count of the divisors of the first 100 positive integers
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# returns the number of divisors of v
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local proc divisor_count( v :: number ) :: number
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# numtheory.ifactors will return something like (e.g., for 24): [1, [[2, 3], [3, 1]]]
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local total := 1;
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if v > 1 then
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local constant factors := numtheory.ifactors( v );
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for f to size factors[ 2 ] do
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total *:= factors[ 2, f, 2 ] + 1
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od
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fi;
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return total
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end;
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scope
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local constant limit := 100;
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printf( "Count of divisors for the first %d positive integers:\n", limit );
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for n to limit do
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printf( "%3d", divisor_count( n ) );
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if n mod 20 = 0 then print() else printf( " " ) fi
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od
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end
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end
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65
Task/Tau-function/COBOL/tau-function.cob
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65
Task/Tau-function/COBOL/tau-function.cob
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@ -0,0 +1,65 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. TAU-FUNCTION.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 TAU-VARS.
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03 TOTAL PIC 999.
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03 N PIC 999.
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03 FILLER REDEFINES N.
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05 FILLER PIC 99.
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05 FILLER PIC 9.
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88 N-EVEN VALUES 0, 2, 4, 6, 8.
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03 P PIC 999.
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03 P-SQUARED PIC 999.
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03 N-DIV-P PIC 999V999.
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03 FILLER REDEFINES N-DIV-P.
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05 NEXT-N PIC 999.
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05 FILLER PIC 999.
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88 DIVISIBLE VALUE ZERO.
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03 F-COUNT PIC 999.
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01 CONTROL-VARS.
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03 I PIC 999.
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01 OUT-VARS.
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03 OUT-ITM PIC ZZ9.
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03 OUT-STR PIC X(80) VALUE SPACES.
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03 OUT-PTR PIC 99 VALUE 1.
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PROCEDURE DIVISION.
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BEGIN.
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PERFORM SHOW-TAU VARYING I FROM 1 BY 1
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UNTIL I IS GREATER THAN 100.
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STOP RUN.
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SHOW-TAU.
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MOVE I TO N.
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PERFORM TAU.
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MOVE TOTAL TO OUT-ITM.
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STRING OUT-ITM DELIMITED BY SIZE INTO OUT-STR
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WITH POINTER OUT-PTR.
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IF OUT-PTR IS EQUAL TO 61,
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DISPLAY OUT-STR,
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MOVE 1 TO OUT-PTR.
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TAU.
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MOVE 1 TO TOTAL.
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PERFORM POWER-OF-2 UNTIL NOT N-EVEN.
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MOVE ZERO TO P-SQUARED.
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PERFORM ODD-FACTOR THRU ODD-FACTOR-LOOP
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VARYING P FROM 3 BY 2
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UNTIL P-SQUARED IS GREATER THAN N.
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IF N IS GREATER THAN 1,
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MULTIPLY 2 BY TOTAL.
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POWER-OF-2.
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ADD 1 TO TOTAL.
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DIVIDE 2 INTO N.
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ODD-FACTOR.
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MULTIPLY P BY P GIVING P-SQUARED.
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MOVE 1 TO F-COUNT.
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ODD-FACTOR-LOOP.
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DIVIDE N BY P GIVING N-DIV-P.
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IF DIVISIBLE,
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MOVE NEXT-N TO N,
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ADD 1 TO F-COUNT,
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GO TO ODD-FACTOR-LOOP.
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MULTIPLY F-COUNT BY TOTAL.
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@ -1,18 +1,18 @@
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fun divisorCount = int by int n
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int total = 1
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for ; (n & 1) == 0; n /= 2 do ++total end
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for int p = 3; p * p <= n; p += 2
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int count = 1
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for ; n % p == 0; n /= p do ++count end
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total *= count
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fun divisorCount ← int by int n
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int total ← 1
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for ; (n & 1) æ 0; n /← 2 do ++total end
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for int p ← 3; p * p ≤ n; p +← 2
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int count ← 1
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for ; n % p æ 0; n /← p do ++count end
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total *← count
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end
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if n > 1 do total *= 2 end
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if n > 1 do total *← 2 end
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return total
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end
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int limit = 100
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int limit ← 100
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writeLine("Count of divisors for the first " + limit + " positive integers:")
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for int n = 1; n <= limit; ++n
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text value = text!divisorCount(n)
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for int n ← 1; n ≤ limit; ++n
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text value ← text!divisorCount(n)
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write((" " * (3 - value.length)) + value)
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if n % 20 == 0 do writeLine() end
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if n % 20 æ 0 do writeLine() end
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end
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@ -1,16 +1,17 @@
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func cntdiv n .
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i = 1
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while i <= sqrt n
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if n mod i = 0
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func divcnt n .
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tot = 1
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p = 2
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while p <= sqrt n
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cnt = 1
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while n mod p = 0
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cnt += 1
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if i <> n div i
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cnt += 1
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.
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n /= p
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.
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i += 1
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tot *= cnt
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p += 1
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.
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return cnt
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.
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for i to 100
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write cntdiv i & " "
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if n > 1 : tot *= 2
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return tot
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.
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for i to 100 : write divcnt i & " "
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print ""
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45
Task/Tau-function/Fennel/tau-function.fennel
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45
Task/Tau-function/Fennel/tau-function.fennel
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@ -0,0 +1,45 @@
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(do ;;; find the count of the divisors of the first 100 positive integers
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; returns the number of divisors of v
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(fn divisor-count [v]
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(var (total n) (values 1 v))
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; Deal with powers of 2 first
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(while (= 0 (% n 2))
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(set total (+ total 1))
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(set n (math.floor (/ n 2)))
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)
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; Odd prime factors up to the square root
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(var p 1)
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(while (do (set p (+ p 2))
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(<= (* p p) n)
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)
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(var count 1)
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(while (= 0 (% n p))
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(set count (+ count 1))
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(set n (math.floor (/ n p)))
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)
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(set total (* total count))
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)
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; If n > 1 then it's prime
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(when (> n 1)
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(set total (* total 2))
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)
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total
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)
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(do
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(local limit 100)
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(io.write (.. "Count of divisors for the first " limit " positive integers:\n"))
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(for [n 1 limit]
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(io.write (string.format "%3d%s"
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(divisor-count n)
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(if (= 0 (% n 20))
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"\n"
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;else
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" "
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)
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)
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)
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)
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)
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)
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9
Task/Tau-function/Icon/tau-function.icon
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9
Task/Tau-function/Icon/tau-function.icon
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@ -0,0 +1,9 @@
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procedure main()
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every writes(" ",tau(seq()))\100
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write()
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end
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procedure tau(n)
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every (c := 0, n%(1 to n) = 0, c +:= 1)
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return c
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end
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1
Task/Tau-function/Maxima/tau-function.maxima
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1
Task/Tau-function/Maxima/tau-function.maxima
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@ -0,0 +1 @@
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makelist(cardinality(divisors(i)), i, 1, 100);
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@ -1,6 +1,4 @@
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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;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</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;">"%3d"</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: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</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: #008080;">end</span> <span style="color: #008080;">for</span>
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<!--
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for i=1 to 100 do
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printf(1,"%3d",{length(factors(i,1))})
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if remainder(i,20)=0 then puts(1,"\n") end if
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end for
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@ -1,4 +1,2 @@
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(phixonline)-->
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">100</span><span style="color: #0000FF;">),{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}}),</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%3d"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">r</span><span style="color: #0000FF;">}),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">))</span>
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<!--
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sequence r = apply(apply(true,factors,{tagset(100),{1}}),length)
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puts(1,join_by(apply(true,sprintf,{{"%3d"},r}),1,20,""))
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2
Task/Tau-function/Uiua/tau-function.uiua
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2
Task/Tau-function/Uiua/tau-function.uiua
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@ -0,0 +1,2 @@
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Tau ← -⊃(=|×2/+=0◿⇡₁◌)⟜⌊⊸√
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↯[5 20] ≡Tau ⇡₁100
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