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A300251 Möbius transform of arithmetic derivative (A003415).

%I A300251 #11 Mar 14 2018 03:48:50
%S A300251 0,1,1,3,1,3,1,8,5,5,1,8,1,7,6,20,1,11,1,14,8,11,1,20,9,13,21,20,1,14,
%T A300251 1,48,12,17,10,28,1,19,14,36,1,20,1,32,26,23,1,48,13,29,18,38,1,39,14,
%U A300251 52,20,29,1,36,1,31,36,112,16,32,1,50,24,34,1,68,1,37,38,56,16,38,1,88,81,41,1,52,20,43,30,84,1,50
%N A300251 Möbius transform of arithmetic derivative (A003415).
%H A300251 Antti Karttunen, <a href="/A300251/b300251.txt">Table of n, a(n) for n = 1..65537</a>
%F A300251 a(n) = Sum_{d|n} A008683(n/d)*A003415(d).
%F A300251 a(n) = A003415(n) - A300252(n).
%o A300251 (PARI)
%o A300251 A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
%o A300251 A300251(n) = sumdiv(n,d,moebius(n/d)*A003415(d));
%Y A300251 Cf. A003415, A008683, A300245, A300252, A300253.
%K A300251 nonn
%O A300251 1,4
%A A300251 _Antti Karttunen_, Mar 08 2018