A359937 - OEIS

%I #18 Jan 21 2023 03:31:00

%S 1,3,1,3,6,3,1,3,1,18,1,3,1,3,6,3,18,3,1,18,1,3,1,3,6,29,1,3,1,18,1,3,

%T 1,20,6,3,38,3,1,18,1,3,1,3,6,3,1,3,1,68,18,29,1,3,6,3,1,3,1,18,1,3,1,

%U 3,71,3,1,20,1,18,1,3,1,40,6,3,1,29,1,18,1,85,1,3

%N a(n) = Sum_{d|n, d-1 is square} d.

%H Seiichi Manyama, <a href="/A359937/b359937.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: Sum_{k>=0} (k^2+1) * x^(k^2+1)/(1 - x^(k^2+1)).

%F Sum_{k=1..n} a(k) ~ zeta(3/2)*n^(3/2)/3. - _Vaclav Kotesovec_, Jan 21 2023

%t Table[Sum[If[IntegerQ[Sqrt[d-1]], d, 0], {d, Divisors[n]}], {n, 1, 100}] (* _Vaclav Kotesovec_, Jan 21 2023 *)

%o (PARI) a(n) = sumdiv(n, d, issquare(d-1)*d);

%o (PARI) my(N=100, x='x+O('x^N)); Vec(sum(k=0, sqrtint(N), (k^2+1)*x^(k^2+1)/(1-x^(k^2+1))))

%Y Cf. A002522, A035316, A359967.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 19 2023