cp's OEIS Frontend

A374974 a(n) = Sum_{k=1..n-1} sigma(k) * sigma_2(n-k).

%I A374974 #20 Sep 20 2024 06:18:50
%S A374974 0,1,8,29,78,170,324,579,918,1472,2106,3126,4174,5904,7500,10189,
%T A374974 12458,16563,19574,25312,29538,37320,42456,53472,59456,73482,81806,
%U A374974 99268,108352,132084,141814,170411,184076,217438,231322,276579,289408,340624,361128,419734
%N A374974 a(n) = Sum_{k=1..n-1} sigma(k) * sigma_2(n-k).
%C A374974 Convolution of sigma with sigma_2.
%H A374974 Vaclav Kotesovec, <a href="/A374974/b374974.txt">Table of n, a(n) for n = 1..10000</a>
%F A374974 G.f.: ( Sum_{k>=1} k * x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ).
%F A374974 Sum_{k=1..n} a(k) ~  Pi^2 * zeta(3) * n^5 / 360. - _Vaclav Kotesovec_, Sep 19 2024
%t A374974 Table[Sum[DivisorSigma[1, k]*DivisorSigma[2, n-k], {k, 1, n-1}], {n, 1, 50}] (* _Vaclav Kotesovec_, Sep 19 2024 *)
%o A374974 (PARI) a(n) = sum(k=1, n-1, sigma(k, 1)*sigma(n-k, 2));
%o A374974 (PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, k*x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k))))
%Y A374974 Cf. A000203, A001157, A374963, A374973, A376290.
%K A374974 nonn,easy
%O A374974 1,3
%A A374974 _Seiichi Manyama_, Jul 26 2024