cp's OEIS Frontend

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

%I A190119 #22 Jul 25 2024 06:58:22
%S A190119 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,
%T A190119 114,115,123,124,155,156,161,175,194,206,211,212,233,249,266,267,308,
%U A190119 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
%N A190119 a(n) = Sum_{k=1..n} lcm(k,k')/k, where k' is arithmetic derivative of k.
%C A190119 Use lcm(1,0)=0.
%H A190119 G. C. Greubel, <a href="/A190119/b190119.txt">Table of n, a(n) for n = 1..10000</a>
%e A190119 lcm(1,1')/1+lcm(2,2')/2+lcm(3,3')/3=0+2/2+3/3=2 ->a(3)=2.
%p A190119 der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
%p A190119 seq(add(lcm(der(i),i)/i,i=1..n),n=1..50);
%t A190119 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 *)
%o A190119 (PARI) {A003415(n, f)=sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])};
%o A190119 for(n=1,20, print1(sum(k=1,n,lcm(k,A003415(k))/k), ", ")) \\ _G. C. Greubel_, Dec 29 2017
%Y A190119 Cf. A003415.
%K A190119 nonn
%O A190119 1,3
%A A190119 _Giorgio Balzarotti_, May 04 2011