Task: Chowla numbers



C#: using System;

namespace chowla_cs
{
    class Program
    {
        static int chowla(int n)
        {
            int sum = 0;
            for (int i = 2, j; i * i <= n; i++)
                if (n % i == 0) sum += i + (i == (j = n / i) ? 0 : j);
            return sum;
        }

        static bool[] sieve(int limit)
        {
            
            
            bool[] c = new bool[limit];
            for (int i = 3; i * 3 < limit; i += 2)
                if (!c[i] && (chowla(i) == 0))
                    for (int j = 3 * i; j < limit; j += 2 * i)
                        c[j] = true;
            return c;
        }

        static void Main(string[] args)
        {
            for (int i = 1; i <= 37; i++)
                Console.WriteLine("chowla({0}) = {1}", i, chowla(i));
            int count = 1, limit = (int)(1e7), power = 100;
            bool[] c = sieve(limit);
            for (int i = 3; i < limit; i += 2)
            {
                if (!c[i]) count++;
                if (i == power - 1)
                {
                    Console.WriteLine("Count of primes up to {0,10:n0} = {1:n0}", power, count);
                    power *= 10;
                }
            }

            count = 0; limit = 35000000;
            int k = 2, kk = 3, p;
            for (int i = 2; ; i++)
            {
                if ((p = k * kk) > limit) break;
                if (chowla(p) == p - 1)
                {
                    Console.WriteLine("{0,10:n0} is a number that is perfect", p);
                    count++;
                }
                k = kk + 1; kk += k;
            }
            Console.WriteLine("There are {0} perfect numbers <= 35,000,000", count);
            if (System.Diagnostics.Debugger.IsAttached) Console.ReadKey();
        }
    }
}









Ada: with Ada.Text_IO;

procedure Chowla_Numbers is

   function Chowla (N : Positive) return Natural is
      Sum : Natural  := 0;
      I   : Positive := 2;
      J   : Positive;
   begin
      while I * I <= N loop
         if N mod I = 0 then
            J   := N / I;
            Sum := Sum + I + (if I = J then 0 else J);
            end if;
            I := I + 1;
      end loop;
      return Sum;
   end Chowla;

   procedure Put_37_First is
      use Ada.Text_IO;
   begin
      for A in Positive range 1 .. 37 loop
         Put_Line ("chowla(" & A'Image & ") = " & Chowla (A)'Image);
      end loop;
   end Put_37_First;

   procedure Put_Prime is
      use Ada.Text_IO;
      Count : Natural  := 0;
      Power : Positive := 100;
   begin
      for N in Positive range 2 .. 10_000_000 loop
         if Chowla (N) = 0 then
            Count := Count + 1;
         end if;
         if N mod Power = 0 then
            Put_Line ("There is " & Count'Image & " primes < " & Power'Image);
            Power := Power * 10;
         end if;
      end loop;
   end Put_Prime;

   procedure Put_Perfect is
      use Ada.Text_IO;
      Count : Natural  := 0;
      Limit : constant := 350_000_000;
      K     : Natural := 2;
      Kk    : Natural := 3;
      P     : Natural;
   begin
      loop
         P := K * Kk;
         exit when P > Limit;

         if Chowla (P) = P - 1 then
            Put_Line (P'Image & " is a perfect number");
            Count := Count + 1;
         end if;
         K  := Kk + 1;
         Kk := Kk + K;
      end loop;
      Put_Line ("There are " & Count'Image & " perfect numbers < " & Limit'Image);
   end Put_Perfect;

begin
   Put_37_First;
   Put_Prime;
   Put_Perfect;
end Chowla_Numbers;