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%I #24 Sep 30 2019 03:14:49
%S 0,2,3,16,5,30,7,96,54,70,11,192,13,126,120,512,17,378,19,480,210,286,
%T 23,1056,250,390,729,896,29,930,31,2560,462,646,420,2160,37,798,624,
%U 2720,41,1722,43,2112,1755,1150,47,5376,686,2250
%N a(n) = n*n', where n' is the arithmetic derivative (A003415) of n.
%C Sequence is not injective. 4153248 is the smallest number that occurs more than once, as a(1368) and as a(2277). See example in A327861. - _Antti Karttunen_, Sep 29 2019
%H G. C. Greubel, <a href="/A190116/b190116.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A085731(n) * A086130(n). - _Michel Marcus_, Oct 24 2013
%e For n=4, 4'= 4, 4*4' = 16, so a(4)=16.
%p der:=n->n*add(op(2,p)/op(1,p),p=ifactors(n)[2]):
%p seq(der(n)*n,n=1..50);
%t A003415[n_]:= If[Abs@n < 2, 0, n Total[#2/#1 & @@@FactorInteger[Abs@n]]]; Table[n*A003415[n], {n, 1, 50}] (* _G. C. Greubel_, Dec 29 2017 *)
%o (PARI) a(n) = n*sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); \\ _Michel Marcus_, Dec 30 2017
%Y Cf. A003415, A327861 (number of times n occurs in this sequence).
%K nonn
%O 1,2
%A _Giorgio Balzarotti_, May 04 2011
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