A190116 - OEIS

A190116

a(n) = n*n', where n' is the arithmetic derivative (A003415) of n.

0, 2, 3, 16, 5, 30, 7, 96, 54, 70, 11, 192, 13, 126, 120, 512, 17, 378, 19, 480, 210, 286, 23, 1056, 250, 390, 729, 896, 29, 930, 31, 2560, 462, 646, 420, 2160, 37, 798, 624, 2720, 41, 1722, 43, 2112, 1755, 1150, 47, 5376, 686, 2250

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OFFSET

1,2

COMMENTS

Sequence is not injective. 4153248 is the smallest number that occurs more than once, as a(1368) and as a(2277). See example in A327861. - Antti Karttunen, Sep 29 2019

LINKS

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

FORMULA

a(n) = A085731(n) * A086130(n). - Michel Marcus, Oct 24 2013

EXAMPLE

For n=4, 4'= 4, 4*4' = 16, so a(4)=16.

MAPLE

der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]):

seq(der(n)*n, n=1..50);

MATHEMATICA

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

PROG