A190117 a(n) = Sum_{k=1..n} k*k', where n' is the arithmetic derivative of n.

0, 2, 5, 21, 26, 56, 63, 159, 213, 283, 294, 486, 499, 625, 745, 1257, 1274, 1652, 1671, 2151, 2361, 2647, 2670, 3726, 3976, 4366, 5095, 5991, 6020, 6950, 6981, 9541, 10003, 10649, 11069, 13229, 13266, 14064, 14688, 17408, 17449, 19171, 19214, 21326, 23081, 24231, 24278, 29654, 30340, 32590

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Example

1*1'+2*2'+3*3'=0+2+3=5 ->a(3)= 5.

Maple

der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):
seq(add(der(i)*i, i=1..n), n=1..50);

Mathematica

A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
Table[Sum[k*A003415[k], {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)

Crossrefs

Cf. A003415, A190116.

Sequence in context: A240147 A358556 A293687 * A230656 A266950 A328689

Adjacent sequences: A190114 A190115 A190116 * A190118 A190119 A190120

Keyword

nonn

Author

Giorgio Balzarotti, May 04 2011

Status

approved