# [seqfan] When n^2 divides sum

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Tue Apr 14 22:42:27 CEST 2009

```I have not yet submitted this first sequence, but I will as soon as someone extends it at least a few more terms (please) so that I can be sure it isn't already in the EIS.

%I A159555
%S A159555 1,6,22
%N A159555 Those n where n^2 divides A159553(n), where A159553(n) = sum{k=0 to n} binomial(n,k) * GCD(n,k).
%C A159555 For the purpose of this sequence, GCD(n,0) = n.
%Y A159555 A159553,A159554,A159458
%K A159555 more,nonn
%O A159555 1,2

I have also submitted the following related sequence, but it hasn't yet appeared in the EIS:

%I A159458
%S A159458 1,2,3,11,33
%N A159458 Those n where n^2 divides A159068(n), where A159068(n) = sum{k=1 to n} binomial(n,k) * GCD(n,k).
%C A159458 n divides A159068(n) for all positive integers n.
%Y A159458 A159068,A159069
%K A159458 more,nonn
%O A159458 1,2

Is there a way to determine the values of these sequences besides trial and error division?

Thanks,
Leroy Quet

```