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A359937 a(n) = Sum_{d|n, d-1 is square} d.

%I A359937 #18 Jan 21 2023 03:31:00
%S A359937 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 A359937 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 A359937 3,71,3,1,20,1,18,1,3,1,40,6,3,1,29,1,18,1,85,1,3
%N A359937 a(n) = Sum_{d|n, d-1 is square} d.
%H A359937 Seiichi Manyama, <a href="/A359937/b359937.txt">Table of n, a(n) for n = 1..10000</a>
%F A359937 G.f.: Sum_{k>=0} (k^2+1) * x^(k^2+1)/(1 - x^(k^2+1)).
%F A359937 Sum_{k=1..n} a(k) ~ zeta(3/2)*n^(3/2)/3. - _Vaclav Kotesovec_, Jan 21 2023
%t A359937 Table[Sum[If[IntegerQ[Sqrt[d-1]], d, 0], {d, Divisors[n]}], {n, 1, 100}] (* _Vaclav Kotesovec_, Jan 21 2023 *)
%o A359937 (PARI) a(n) = sumdiv(n, d, issquare(d-1)*d);
%o A359937 (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 A359937 Cf. A002522, A035316, A359967.
%K A359937 nonn
%O A359937 1,2
%A A359937 _Seiichi Manyama_, Jan 19 2023