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A190118 a(n) = Sum_{k=1..n} k/gcd(k,k'), where n' is arithmetic derivative of n.

%I A190118 #16 Dec 30 2017 03:33:55
%S A190118 1,3,6,7,12,18,25,27,30,40,51,54,67,81,96,97,114,120,139,144,165,187,
%T A190118 210,216,221,247,248,255,284,314,345,347,380,414,449,452,489,527,566,
%U A190118 576,617,659,702,713,728,774,821,824,831,841
%N A190118 a(n) = Sum_{k=1..n} k/gcd(k,k'), where n' is arithmetic derivative of n.
%C A190118 Use gcd(1,0)=1.
%H A190118 G. C. Greubel, <a href="/A190118/b190118.txt">Table of n, a(n) for n = 1..10000</a>
%e A190118 1/gcd(1,1')+2/gcd(2,2')+3/gcd(3,3')=1+2/1+3/1=6 ->a(3)=6.
%p A190118 der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
%p A190118 seq(add(i/gcd(der(i),i),i=1..n),n=1..50);
%t A190118 A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
%t A190118 Table[Sum[k/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Dec 29 2017 *)
%Y A190118 Cf. A003415.
%K A190118 nonn
%O A190118 1,2
%A A190118 _Giorgio Balzarotti_, May 04 2011