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a(n) = Sum_{k=1..10^n} k*sigma(k).
0

%I #16 Dec 20 2018 23:21:16

%S 1,622,558275,549175530,548429473046,548320905633448,

%T 548312690631798482,548311465139943768941,548311366911386862908968,

%U 548311356554322895313137239,548311355740964925044531454428,548311355626818302486560961291870,548311355617569600726982364186141942

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

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

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

%t Array[Sum[k DivisorSigma[1, k], {k, 10^#}] &, 7, 0] (* _Michael De Vlieger_, Nov 20 2018 *)

%o (PARI) a(n) = sum(k=1, 10^n, k*sigma(k)); \\ _Michel Marcus_, Nov 23 2018

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

%K nonn

%O 0,2

%A _Daniel Suteu_, Nov 16 2018