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A190119 a(n) = Sum_{k=1..n} lcm(k,k')/k, where k' is arithmetic derivative of k. 3
0, 1, 2, 3, 4, 9, 10, 13, 15, 22, 23, 27, 28, 37, 45, 47, 48, 55, 56, 62, 72, 85, 86, 97, 99, 114, 115, 123, 124, 155, 156, 161, 175, 194, 206, 211, 212, 233, 249, 266, 267, 308, 309, 321, 334, 359, 360, 367, 369, 378, 398, 412, 413, 416, 432, 455, 477, 508, 509, 532, 533, 566, 583, 586, 604, 665, 666, 684, 710, 769 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Use lcm(1,0)=0.

LINKS

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

EXAMPLE

lcm(1,1')/1+lcm(2,2')/2+lcm(3,3')/3=0+2/2+3/3=2 ->a(3)=2.

MAPLE

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

seq(add(lcm(der(i), 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[LCM[k, A003415[k]]/k, {k, 1, n}], {n, 1, 50}] (* G. C. Greubel, Dec 29 2017 *)

PROG

(PARI) {A003145(n, f)=sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])};

for(n=1, 20, print1(sum(k=1, n, lcm(k, A003145(k))/k), ", ")) \\ G. C. Greubel, Dec 29 2017

CROSSREFS

Cf. A003415.

Sequence in context: A007498 A073338 A200260 * A273907 A066105 A083180

Adjacent sequences:  A190116 A190117 A190118 * A190120 A190121 A190122

KEYWORD

nonn

AUTHOR

Giorgio Balzarotti, May 04 2011

STATUS

approved

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Last modified September 26 22:43 EDT 2021. Contains 347672 sequences. (Running on oeis4.)