[seqfan] Re: sequence, array, some questions

[Robert Israel]

On Sat, 6 Mar 2010, Kimberling, Clark wrote:

> Seqfans,
>
> Let a(n) be the number of positive integers k such that n+k divides n*k.
> (Equivalently, 1/n + 1/k = 1/m for some integer m.) The first 30 terms
> of a(n) are 0,1,1,2,1,3,1,3,2,4,1,5,1,4,3,4,1,6,1,6,4,4,1,8,2,4,3,6,1,10
> .

There are several mistakes here.  For example, a(6) should be 4, not, 3, 
as 6+k divides 6*k for k = 3, 6, 12 and 30.  If I'm not mistaken, the 
first 30 terms should be

0, 1, 1, 2, 1, 4, 1, 3, 2, 4, 1, 7, 1, 4, 4, 4, 1, 7, 1, 7, 4, 4, 1, 10, 
2, 4, 3, 7, 1, 13

A Maple program to calculate a(n) is

A:= n -> nops(remove(hastype,[isolve((n+k)*x=n*k)],nonposint));

Cheers,
Robert Israel