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%I #21 May 08 2021 07:39:51
%S 1,10,17,59,37,170,65,284,186,370,145,1003,197,650,629,1245,325,1860,
%T 401,2183,1105,1450,577,4828,998,1970,1786,3835,901,6290,1025,5214,
%U 2465,3250,2405,10974,1445,4010,3349,10508,1765,11050,1937,8555,6882
%N a(n) = Sum_{d|n} sigma(d)^2.
%H Harry J. Smith, <a href="/A065018/b065018.txt">Table of n, a(n) for n = 1..1000</a>
%F Dirichlet convolution of A072861 and A000012. Dirichlet g.f.: zeta^2(s)*zeta^2(s-1)*zeta(s-2)/zeta(2s-2). - _R. J. Mathar_, Feb 03 2011
%F Sum_{k=1..n} a(k) ~ 5 * Zeta(3)^2 * n^3 / 6. - _Vaclav Kotesovec_, Feb 01 2019
%F From _Seiichi Manyama_, May 08 2021: (Start)
%F G.f.: Sum_{k >= 1} sigma(k)^2 * x^k/(1 - x^k).
%F If p is prime, a(p) = 1 + (p+1)^2. (End)
%o (PARI) { for (n=1, 1000, a=sumdiv(n, d, sigma(d)^2); write("b065018.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 03 2009
%o (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^2*x^k/(1-x^k))) \\ _Seiichi Manyama_, May 08 2021
%Y Cf. A029939, A062367.
%K mult,nonn
%O 1,2
%A _Vladeta Jovovic_, Nov 19 2001
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