A356042 a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).
1, 7, 18, 45, 72, 138, 189, 301, 403, 565, 688, 985, 1156, 1462, 1759, 2212, 2503, 3115, 3478, 4207, 4768, 5506, 6037, 7269, 7947, 8973, 9895, 11272, 12115, 13897, 14860, 16678, 18031, 19777, 21154, 23908, 25279, 27457, 29338, 32362, 34045, 37411, 39262, 42583
Offset: 1
Keywords
Programs
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Mathematica
Table[Sum[DivisorSigma[2, k]*Floor[n/k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Aug 07 2022 *) -
PARI
a(n) = sum(k=1, n, sigma(k, 2)*(n\k));
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PARI
a(n) = sum(k=1, n, sumdiv(k, d, d^2*numdiv(k/d)));
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PARI
my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, 2)*x^k/(1-x^k))/(1-x))
Formula
a(n) = Sum_{k=1..n} Sum_{d|k} d^2 * tau(k/d).
G.f.: (1/(1-x)) * Sum_{k>=1} sigma_2(k) * x^k/(1 - x^k).
a(n) ~ zeta(3)^2 * n^3 / 3. - Vaclav Kotesovec, Aug 07 2022