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();
        }
    }
}


Go: package main

import "fmt"

func chowla(n int) int {
    if n < 1 {
        panic("argument must be a positive integer")
    }
    sum := 0
    for i := 2; i*i <= n; i++ {
        if n%i == 0 {
            j := n / i
            if i == j {
                sum += i
            } else {
                sum += i + j
            }
        }
    }
    return sum
}

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

func commatize(n int) string {
    s := fmt.Sprintf("%d", n)
    le := len(s)
    for i := le - 3; i >= 1; i -= 3 {
        s = s[0:i] + "," + s[i:]
    }
    return s
}

func main() {
    for i := 1; i <= 37; i++ {
        fmt.Printf("chowla(%2d) = %d\n", i, chowla(i))
    }
    fmt.Println()

    count := 1
    limit := int(1e7)
    c := sieve(limit)
    power := 100
    for i := 3; i < limit; i += 2 {
        if !c[i] {
            count++
        }
        if i == power-1 {
            fmt.Printf("Count of primes up to %-10s = %s\n", commatize(power), commatize(count))
            power *= 10
        }
    }

    fmt.Println()
    count = 0
    limit = 35000000
    for i := uint(2); ; i++ {
        p := 1 << (i - 1) * (1<<i - 1) 
        if p > limit {
            break
        }
        if chowla(p) == p-1 {
            fmt.Printf("%s is a perfect number\n", commatize(p))
            count++
        }
    }
    fmt.Println("There are", count, "perfect numbers <= 35,000,000")
}