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

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

(PARI) a(n) = n*sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); \\ Michel Marcus, Dec 30 2017

Crossrefs

Cf. A003415, A327861 (number of times n occurs in this sequence).

Sequence in context: A209593 A054496 A351748 * A088447 A326578 A103390

Adjacent sequences: A190113 A190114 A190115 * A190117 A190118 A190119

Keyword

nonn

Author

Giorgio Balzarotti, May 04 2011

Status

approved