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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.)