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A188138 Sum of sigma_2(k) for 1 <= k <= 10^n, where sigma_2(k) is the sum of the divisors of k squared. 2

%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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Last modified June 8 20:17 EDT 2024. Contains 373227 sequences. (Running on oeis4.)