A321675 a(n) = Sum_{k=1..10^n} k*sigma(k).

1, 622, 558275, 549175530, 548429473046, 548320905633448, 548312690631798482, 548311465139943768941, 548311366911386862908968, 548311356554322895313137239, 548311355740964925044531454428, 548311355626818302486560961291870, 548311355617569600726982364186141942

Offset: 0

Author

Daniel Suteu, Nov 16 2018

Keywords

• nonn

Crossrefs

Cf. A000203, A064987, A072692, A086463 (Pi^2/18), A143128.

Programs

Mathematica

Array[Sum[k DivisorSigma[1, k], {k, 10^#}] &, 7, 0] (* Michael De Vlieger, Nov 20 2018 *)

PARI

a(n) = sum(k=1, 10^n, k*sigma(k)); \\ Michel Marcus, Nov 23 2018

Formula

a(n) = A143128(10^n).

a(n) ~ 10^(3*n) * Pi^2 / 18.