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

1, 469, 407819, 401382971, 400757638164, 400692683389101, 400686363385965077, 400685705322499946270, 400685641565621401132515, 400685635084923815073475174, 400685634458741808360827818508, 400685634393583522561137962683069

Offset: 0

Author

Robert G. Wilson v, Apr 25 2011

Keywords

• nonn

Comments

a(n) ~ 10^(3n)*zeta(3)/3.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..18

Crossrefs

Cf. A072692.

Programs

Mathematica

k = 1; lst = {}; s = 0; Do[ While[k < 10^n + 1, s = s + DivisorSigma[2, k]; k++]; AppendTo[lst, s], {n, 0, 9}]; lst
a[n_] := With[{nn=10^n}, Sum[Floor[nn/k]*k^2, {k, nn}]]; Array[a,9,0] (* T. D. Noe, Apr 25 2011 *)

Extensions

a(10)-a(11) from Hiroaki Yamanouchi, Jul 06 2014