Data update

Task/Chowla-numbers/EMal/chowla-numbers.emal

@@ -1,44 +1,44 @@
-fun chowla = int by int n
-  int sum = 0
-  int j = 0
-  for int i = 2; i * i <= n; i++ do
-    if n % i == 0 do sum += i + when(i == (j = n / i), 0, j) end
+fun chowla ← int by int n
+  int sum ← 0
+  int j ← 0
+  for int i ← 2; i * i ≤ n; ++i do
+    if n % i æ 0 do sum += i + when(i æ (j ← n / i), 0, j) end
   end
   return sum
 end
-fun sieve = List by int limit
-  List c = logic[].with(limit)
-  for int i = 3; i * 3 < limit; i += 2
-    if c[i] or chowla(i) != 0 do continue end
-    for int j = 3 * i; j < limit; j += 2 * i do c[j] = true end
+fun sieve ← List by int limit
+  List c ← logic[].with(limit)
+  for int i ← 3; i * 3 < limit; i += 2
+    if c[i] or chowla(i) ≠ 0 do continue end
+    for int j ← 3 * i; j < limit; j += 2 * i do c[j] ← true end
   end
   return c
 end
 # find and display (1 per line) for the 1st 37 integers
-for int i = 1; i <= 37; i++ do writeLine("chowla(" + i + ") = " + chowla(i)) end
-int count = 1
-int limit = 10000000
-int power = 100
-List c = sieve(limit)
-for int i = 3; i < limit; i += 2
-  if not c[i] do count++ end
-  if i == power - 1
-    writeLine("Count of primes up to " + power + " = " + count)
+for int i ← 1; i ≤ 37; ++i do writeLine("chowla(" + i + ") = ", chowla(i)) end
+int count ← 1
+int limit ← 10000000
+int power ← 100
+List c ← sieve(limit)
+for int i ← 3; i < limit; i += 2
+  if not c[i] do ++count end
+  if i æ power - 1
+    writeLine("Count of primes up to ", power, " = ", count)
     power *= 10
   end
 end
-count = 0
-limit = 35000000
-int k = 2
-int kk = 3
+count ← 0
+limit ← 35000000
+int k ← 2
+int kk ← 3
 int p
-for int i = 2; ; i++
-  if (p = k * kk) > limit do break end
-  if chowla(p) == p - 1
-    writeLine(p + " is a number that is perfect")
-    count++
+for int i ← 2; ; ++i
+  if (p ← k * kk) > limit do break end
+  if chowla(p) æ p - 1
+    writeLine(p, " is a number that is perfect")
+    ++count
   end
-  k = kk + 1
+  k ← kk + 1
   kk += k
 end
-writeLine("There are " + count + " perfect numbers <= 35,000,000")
+writeLine("There are ", count, " perfect numbers ≤ 35,000,000")

Task/Chowla-numbers/PascalABC.NET/chowla-numbers.pas

@@ -0,0 +1,54 @@
+function chowla(n: Integer): Integer;
+begin
+  result := 0;
+  var i := 2;
+  while i * i <= n do
+  begin
+    if n mod i = 0 then
+      result += i + (if i = n div i then 0 else n div i);
+    i += 1
+  end;
+end;
+
+function sieve(limit: Integer): array of Boolean;
+begin
+  result := new Boolean[limit];
+  for var i := 3 to limit div 3 step 2 do
+    if not result[i] and (chowla(i) = 0) Then
+      for var j := 3 * i to limit step 2 * i do
+        result[j] := true;
+end;
+
+begin
+  for var i := 1 To 37 do
+    WriteLn('chowla(', i, ') = ', chowla(i));
+
+  var count := 1;
+  var limit := 10_000_000;
+  var power := 100;
+  var c := sieve(limit);
+  for var i := 3 To limit Step 2 do
+  begin
+    if not c[i] Then count += 1;
+    if i = power - 1 Then begin
+      WriteLn('Count of primes up to ', power:8, ' = ', count);
+      power *= 10;
+    end;
+  end;
+
+  count := 0;
+  limit := 35_000_000;
+  var k := 2; var kk := 3;
+  while True do
+  begin
+    var p := k * kk;
+    if p > limit Then break;
+    if chowla(p) = p - 1 Then begin
+      WriteLn(p:8, ' is a number that is perfect');
+      count += 1;
+    end;
+    k := kk + 1;
+    kk += k;
+  end;
+  WriteLn('There are ', count, ' perfect numbers <= 35,000,000')
+end.

Task/Chowla-numbers/REXX/chowla-numbers-2.rexx

@@ -0,0 +1,81 @@
+include Settings
+
+say version; say 'Chowla numbers'; say
+numeric digits 12
+call ChowlaNumbers
+call PrimeCount
+call PerfectNumbers
+exit
+
+ChowlaNumbers:
+procedure expose glob.
+call Time('r'); sep = Copies('-',12)
+say sep; say ' n Chowla(n)'; say sep
+m = 37
+do i = 1 to m
+   say Right(i,2) Right(Chowla(i),9)
+end
+say sep
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+PrimeCount:
+procedure expose glob. work.
+call Time('r'); sep = Copies('-',17)
+say sep; say Right('n',8) Right('Primes<n',8); say sep
+d = 1; work. = 1; m = 1e7; n = 0
+do i = 1 by 2 to m+1
+   e = Xpon(i)
+   if e > d then do
+      say Right(10**e,8) Right(n,8)
+      d = e
+   end
+   if work.i = 0 then
+      iterate i
+   if Chowla(i) = 0 then do
+      n = n+1
+      if i > 1 then do
+         j = i+i
+         do while j < m
+            work.j = 0; j = j+i
+         end
+      end
+   end
+end
+say sep
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+PerfectNumbers:
+procedure expose divi.
+call Time('r'); sep = Copies('-',12)
+say sep; say Right('Perfect',12); say sep
+k = 2; kk = 3; m = 140e9; n = 0
+do forever
+   p = k * kk
+   if p > 140e9 then
+      leave
+   if Chowla(p) = p-1 then do
+      n = n+1
+      say Right(p,12)
+   end
+   k = kk+1; kk = kk+k
+end
+say sep
+say n 'perfect numbers found below 140e9'
+say Format(Time('e'),,3) 'seconds'
+say
+return
+
+Chowla:
+/* Chowla numbers */
+procedure expose divi.
+arg x
+/* Formula */
+return Aliquot(x)-1
+
+include Numbers
+include Functions
+include Abend