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A359967 a(n) = Sum_{d|n, d+1 is square} d.

%I A359967 #19 Jan 21 2023 03:52:17
%S A359967 0,0,3,0,0,3,0,8,3,0,0,3,0,0,18,8,0,3,0,0,3,0,0,35,0,0,3,0,0,18,0,8,3,
%T A359967 0,35,3,0,0,3,8,0,3,0,0,18,0,0,83,0,0,3,0,0,3,0,8,3,0,0,18,0,0,66,8,0,
%U A359967 3,0,0,3,35,0,35,0,0,18,0,0,3,0,88,3,0,0,3,0,0
%N A359967 a(n) = Sum_{d|n, d+1 is square} d.
%H A359967 Seiichi Manyama, <a href="/A359967/b359967.txt">Table of n, a(n) for n = 1..10000</a>
%H A359967 Vaclav Kotesovec, <a href="/A359967/a359967.jpg">Plot of Sum_{k=1..n} a(k) / n^(3/2) for n = 1..10^7</a>
%F A359967 G.f.: Sum_{k>=2} (k^2-1) * x^(k^2-1)/(1 - x^(k^2-1)).
%F A359967 Sum_{k=1..n} a(k) ~ zeta(3/2)*n^(3/2)/3. - _Vaclav Kotesovec_, Jan 21 2023
%t A359967 Table[Sum[If[IntegerQ[Sqrt[d+1]], d, 0], {d, Divisors[n]}], {n, 1, 100}] (* _Vaclav Kotesovec_, Jan 21 2023 *)
%o A359967 (PARI) a(n) = sumdiv(n, d, issquare(d+1)*d);
%o A359967 (PARI) my(N=100, x='x+O('x^N)); concat([0, 0], Vec(sum(k=2, sqrtint(N+1), (k^2-1)*x^(k^2-1)/(1-x^(k^2-1)))))
%Y A359967 Cf. A005563, A035316, A179952, A359937.
%K A359967 nonn
%O A359967 1,3
%A A359967 _Seiichi Manyama_, Jan 20 2023