cp's OEIS Frontend

A190122 a(n) = Sum_{k=1..n} k*lcm(k,k')/gcd(k,k'), where k' is arithmetic derivative of k.

%I A190122 #20 Dec 30 2017 09:32:51
%S A190122 0,4,13,17,42,222,271,319,373,1073,1194,1338,1507,3271,5071,5103,5392,
%T A190122 6148,6509,7109,11519,17811,18340,19924,20174,30314,30341,31909,32750,
%U A190122 60650,61611,61931,77177,99141,113841,114381,115750,146074,170410,177210,178891
%N A190122 a(n) = Sum_{k=1..n} k*lcm(k,k')/gcd(k,k'), where k' is arithmetic derivative of k.
%C A190122 Use lcm(1,0)=0 and gcd(1,0)=1.
%H A190122 G. C. Greubel, <a href="/A190122/b190122.txt">Table of n, a(n) for n = 1..10000</a>
%F A190122 a(n) = Sum_{k=1..n} k*A189036(k).
%e A190122 lcm(1,1')/gcd(1,1')*1+lcm(2,2')/gcd(2,2')*2+lcm(3,3')/gcd(3,3')*3=0+2/1*2+3/1*3=13 ->a(3)=13.
%p A190122 der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
%p A190122 seq(add(lcm(der(i),i)/gcd(der(i),i)*i,i=1..n),n=1..50);
%t A190122 A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
%t A190122 Table[Sum[k*LCM[k, A003415[k]]/GCD[k, A003415[k]], {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Dec 29 2017 *)
%Y A190122 Cf. A003415, A189036, A190118, A190119, A190120.
%K A190122 nonn
%O A190122 1,2
%A A190122 _Giorgio Balzarotti_, May 04 2011