cp's OEIS Frontend

A300253 GCD of arithmetic derivative (A003415) and its Möbius transform (A300251).

%I A300253 #11 Mar 14 2018 03:49:03
%S A300253 0,1,1,1,1,1,1,4,1,1,1,8,1,1,2,4,1,1,1,2,2,1,1,4,1,1,3,4,1,1,1,16,2,1,
%T A300253 2,4,1,1,2,4,1,1,1,16,13,1,1,16,1,1,2,2,1,3,2,4,2,1,1,4,1,1,3,16,2,1,
%U A300253 1,2,2,1,1,4,1,1,1,8,2,1,1,88,27,1,1,4,2,1,2,28,1,1,2,4,2,1,2,16,1,11,1,2,1,1,1,4,1
%N A300253 GCD of arithmetic derivative (A003415) and its Möbius transform (A300251).
%H A300253 Antti Karttunen, <a href="/A300253/b300253.txt">Table of n, a(n) for n = 1..65537</a>
%F A300253 a(n) = gcd(A003415(n), A300251(n)) = gcd(A003415(n), A300252(n)).
%o A300253 (PARI)
%o A300253 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 A300253 A300251(n) = sumdiv(n,d,moebius(n/d)*A003415(d));
%o A300253 A300253(n) = gcd(A003415(n), A300251(n));
%Y A300253 Cf. A003415, A085731, A300245, A300251, A300252.
%K A300253 nonn
%O A300253 1,8
%A A300253 _Antti Karttunen_, Mar 08 2018