A359967 a(n) = Sum_{d|n, d+1 is square} d.
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, 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, 3, 0, 0, 3, 35, 0, 35, 0, 0, 18, 0, 0, 3, 0, 88, 3, 0, 0, 3, 0, 0
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..10000
- Vaclav Kotesovec, Plot of Sum_{k=1..n} a(k) / n^(3/2) for n = 1..10^7
Programs
-
Mathematica
Table[Sum[If[IntegerQ[Sqrt[d+1]], d, 0], {d, Divisors[n]}], {n, 1, 100}] (* Vaclav Kotesovec, Jan 21 2023 *) -
PARI
a(n) = sumdiv(n, d, issquare(d+1)*d);
-
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)))))
Formula
G.f.: Sum_{k>=2} (k^2-1) * x^(k^2-1)/(1 - x^(k^2-1)).
Sum_{k=1..n} a(k) ~ zeta(3/2)*n^(3/2)/3. - Vaclav Kotesovec, Jan 21 2023