%I #14 Mar 10 2023 10:26:18

%S 1,81,784,5329,15876,63504,118336,342225,573049,1285956,1774224,

%T 4177936,4831204,9585216,12446784,21911761,24147396,46416969,47059600,

%U 84603204,92775424,143712144,148060224,268304400,248094001,391327524,417793600,630612544,594872100

%N a(n) = sigma_3(n)^2.

%H Amiram Eldar, <a href="/A356534/b356534.txt">Table of n, a(n) for n = 1..10000</a>

%H Ramanujan's Papers, <a href="http://ramanujan.sirinudi.org/Volumes/published/ram17.html">Some formulas in the analytic theory of numbers</a>, Messenger of Mathematics, XLV, 1916, 81-84, Formula (15), a=b=3.

%F Dirichlet g.f.: zeta(s) * zeta(s-3)^2 * zeta(s-6) / zeta(2*s-6).

%F Multiplicative with a(p^e) = ((p^(3*e+3)-1)/(p^3-1))^2. - _Amiram Eldar_, Aug 11 2022

%t Table[DivisorSigma[3, n]^2, {n, 1, 40}]

%o (PARI) a(n) = sigma(n, 3)^2; \\ _Michel Marcus_, Aug 11 2022

%Y Cf. A001158, A127473, A035116, A072861, A356536 (partial sums).

%K nonn,mult

%O 1,2

%A _Vaclav Kotesovec_, Aug 11 2022