Sequence: smallest number greater than previous term with exactly n divisors: Difference between revisions

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done...
done...
</pre>

=={{header|Sidef}}==
a(n) is the smallest number with exactly n divisors (A005179).
<lang ruby>func nth_divisors(n) {
1..Inf -> first_by { .sigma0 == n }
}

say 15.of { nth_divisors(_+1) }</lang>

{{out}}
<pre>
[1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, 60, 4096, 192, 144]
</pre>

a(n) is the smallest number > a(n-1) with exactly n divisors (A069654).

<lang ruby>func nth_divisors(from=1, n) {
from..Inf -> first_by { .sigma0 == n }
}

with (1) { |from|
say 15.of { from = nth_divisors(from, _+1) }
}</lang>
{{out}}
<pre>
[1, 2, 4, 6, 16, 18, 64, 66, 100, 112, 1024, 1035, 4096, 4288, 4624]
</pre>
</pre>

Revision as of 10:59, 9 April 2019

Sequence: smallest number greater than previous term with exactly n divisors is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The Anti-primes Plus sequence are the natural numbers in which each nth item has n factors, including 1 and itself.

Task

Show the first 15 items of this sequence.

Go

<lang go>package main

import "fmt"

func countDivisors(n int) int { 

   count := 0
   for i := 1; i*i <= n; i++ {
       if n%i == 0 {
           if i == n/i {
               count++
           } else {
               count += 2
           }
       }
   }
   return count

}

func main() { 

   const max = 15
   fmt.Println("The first", max, "anti-primes plus are:")
   for i, next := 1, 1; next <= max; i++ {
       if next == countDivisors(i) {
           fmt.Printf("%d ", i)
           next++
       }
   }
   fmt.Println()

}</lang>

Output:
The first 15 anti-primes plus are:
1 2 4 6 16 18 64 66 100 112 1024 1035 4096 4288 4624

Ring

<lang ring>

  1. Project : ANti-primes

see "working..." + nl see "wait for done..." + nl + nl see "the first 15 Anti-primes Plus are:" + nl + nl num = 1 n = 0 result = list(15) while num < 16 

     n = n + 1
     div = factors(n)
     if div = num
        result[num] = n
        num = num + 1
     ok

end see "[" for n = 1 to len(result) 

   if n < len(result)
      see string(result[n]) + ","
   else
      see string(result[n]) + "]" + nl + nl
   ok

next see "done..." + nl

func factors(an) 

    ansum = 2
    if an < 2
       return(1)
    ok
    for nr = 2 to an/2
        if an%nr = 0
           ansum = ansum+1
        ok
    next
    return ansum

</lang>

Output:
working...
wait for done...

the first 15 Anti-primes Plus are:

[1,2,4,6,16,18,64,66,100,112,1024,1035,4096,4288,4624]

done...

Sidef

a(n) is the smallest number with exactly n divisors (A005179). <lang ruby>func nth_divisors(n) { 

   1..Inf -> first_by { .sigma0 == n }

}

say 15.of { nth_divisors(_+1) }</lang>

Output:
[1, 2, 4, 6, 16, 12, 64, 24, 36, 48, 1024, 60, 4096, 192, 144]

a(n) is the smallest number > a(n-1) with exactly n divisors (A069654).

<lang ruby>func nth_divisors(from=1, n) { 

   from..Inf -> first_by { .sigma0 == n }

}

with (1) { |from| 

   say 15.of { from = nth_divisors(from, _+1) }

}</lang>

Output:
[1, 2, 4, 6, 16, 18, 64, 66, 100, 112, 1024, 1035, 4096, 4288, 4624]
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