cp's OEIS Frontend

A356042 a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).

%I A356042 #15 Aug 07 2022 04:07:52
%S A356042 1,7,18,45,72,138,189,301,403,565,688,985,1156,1462,1759,2212,2503,
%T A356042 3115,3478,4207,4768,5506,6037,7269,7947,8973,9895,11272,12115,13897,
%U A356042 14860,16678,18031,19777,21154,23908,25279,27457,29338,32362,34045,37411,39262,42583
%N A356042 a(n) = Sum_{k=1..n} sigma_2(k) * floor(n/k).
%F A356042 a(n) = Sum_{k=1..n} Sum_{d|k} d^2 * tau(k/d).
%F A356042 G.f.: (1/(1-x)) * Sum_{k>=1} sigma_2(k) * x^k/(1 - x^k).
%F A356042 a(n) ~ zeta(3)^2 * n^3 / 3. - _Vaclav Kotesovec_, Aug 07 2022
%t A356042 Table[Sum[DivisorSigma[2, k]*Floor[n/k], {k, 1, n}], {n, 1, 50}] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o A356042 (PARI) a(n) = sum(k=1, n, sigma(k, 2)*(n\k));
%o A356042 (PARI) a(n) = sum(k=1, n, sumdiv(k, d, d^2*numdiv(k/d)));
%o A356042 (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, 2)*x^k/(1-x^k))/(1-x))
%Y A356042 Partial sums of A007433.
%Y A356042 Column k=2 of A356045.
%Y A356042 Cf. A000005 (tau).
%K A356042 nonn
%O A356042 1,2
%A A356042 _Seiichi Manyama_, Jul 24 2022