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%I #15 Dec 31 2017 01:40:32
%S 0,2,5,21,26,56,63,159,213,283,294,486,499,625,745,1257,1274,1652,
%T 1671,2151,2361,2647,2670,3726,3976,4366,5095,5991,6020,6950,6981,
%U 9541,10003,10649,11069,13229,13266,14064,14688,17408,17449,19171,19214,21326,23081,24231,24278,29654,30340,32590
%N a(n) = Sum_{k=1..n} k*k', where n' is the arithmetic derivative of n.
%H G. C. Greubel, <a href="/A190117/b190117.txt">Table of n, a(n) for n = 1..10000</a>
%e 1*1'+2*2'+3*3'=0+2+3=5 ->a(3)= 5.
%p der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
%p seq(add(der(i)*i,i=1..n),n=1..50);
%t A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]];
%t Table[Sum[k*A003415[k], {k, 1, n}], {n, 1, 50}] (* _G. C. Greubel_, Dec 29 2017 *)
%Y Cf. A003415, A190116.
%K nonn
%O 1,2
%A _Giorgio Balzarotti_, May 04 2011