A190119 a(n) = Sum_{k=1..n} lcm(k,k')/k, where k' is arithmetic derivative of k.

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

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 * A357056 A273907 A066105

Adjacent sequences: A190116 A190117 A190118 * A190120 A190121 A190122

Keyword

nonn

Author

Giorgio Balzarotti, May 04 2011

Status

approved