Numbers whose count of divisors is prime: Difference between revisions

</pre>

=={{header|Go}}==

{{libheader|Go-rcu}}

<lang go>package main

import (

"fmt"

"math"

"rcu"

)

func countDivisors(n int) int {

count := 0

i := 1

k := 1

if n%2 == 1 {

k = 2

}

for ; i <= int(math.Sqrt(float64(n))); i += k {

if n%i == 0 {

count++

j := n / i

if j != i {

count++

}

}

}

return count

}

func main() {

const limit = 1e5

var results []int

for i := 3; i < limit; i++ {

n := countDivisors(i)

if n > 2 && rcu.IsPrime(n) {

results = append(results, i)

}

}

climit := rcu.Commatize(limit)

fmt.Printf("Positive integers under %7s whose number of divisors is an odd prime:\n", climit)

under1000 := 0

for i, n := range results {

fmt.Printf("%7s", rcu.Commatize(n))

if (i+1)%10 == 0 {

fmt.Println()

}

if n < 1000 {

under1000++

}

}

fmt.Printf("\n\nFound %d such integers (%d under 1,000).\n", len(results), under1000)

}</lang>

{{out}}

<pre>

Positive integers under 100,000 whose number of divisors is an odd prime:

4 9 16 25 49 64 81 121 169 289

361 529 625 729 841 961 1,024 1,369 1,681 1,849

2,209 2,401 2,809 3,481 3,721 4,096 4,489 5,041 5,329 6,241

6,889 7,921 9,409 10,201 10,609 11,449 11,881 12,769 14,641 15,625

16,129 17,161 18,769 19,321 22,201 22,801 24,649 26,569 27,889 28,561

29,929 32,041 32,761 36,481 37,249 38,809 39,601 44,521 49,729 51,529

52,441 54,289 57,121 58,081 59,049 63,001 65,536 66,049 69,169 72,361

73,441 76,729 78,961 80,089 83,521 85,849 94,249 96,721 97,969

Found 79 such integers (16 under 1,000).