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%I #31 Dec 24 2016 22:23:43
%S 1,469,407819,401382971,400757638164,400692683389101,
%T 400686363385965077,400685705322499946270,400685641565621401132515,
%U 400685635084923815073475174,400685634458741808360827818508,400685634393583522561137962683069
%N Sum of sigma_2(k) for 1 <= k <= 10^n, where sigma_2(k) is the sum of the divisors of k squared.
%C a(n) ~ 10^(3n)*zeta(3)/3.
%H Hiroaki Yamanouchi, <a href="/A188138/b188138.txt">Table of n, a(n) for n = 0..18</a>
%t k = 1; lst = {}; s = 0; Do[ While[k < 10^n + 1, s = s + DivisorSigma[2, k]; k++]; AppendTo[lst, s], {n, 0, 9}]; lst
%t a[n_] := With[{nn=10^n}, Sum[Floor[nn/k]*k^2, {k, nn}]]; Array[a,9,0] (* _T. D. Noe_, Apr 25 2011 *)
%Y Cf. A072692.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Apr 25 2011
%E a(10)-a(11) from _Hiroaki Yamanouchi_, Jul 06 2014
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