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A190117 a(n) = Sum_{k=1..n} k*k', where n' is the arithmetic derivative of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A088498 A240147 A293687 * A230656 A266950 A328689

Adjacent sequences:  A190114 A190115 A190116 * A190118 A190119 A190120

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti, May 04 2011

STATUS

approved

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Last modified June 20 04:43 EDT 2021. Contains 345157 sequences. (Running on oeis4.)