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

Author

Giorgio Balzarotti, May 04 2011

Keywords

• nonn

Comments

Use lcm(1,0)=0.

Examples

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

Links

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

Crossrefs

Cf. A003415.

Programs

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 *)

PARI

{A003415(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,A003415(k))/k), ", ")) \\ G. C. Greubel, Dec 29 2017