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A300253 GCD of arithmetic derivative (A003415) and its Möbius transform (A300251). 5

%I #11 Mar 14 2018 03:49:03

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

%H Antti Karttunen, <a href="/A300253/b300253.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = gcd(A003415(n), A300251(n)) = gcd(A003415(n), A300252(n)).

%o (PARI)

%o 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(n) = sumdiv(n,d,moebius(n/d)*A003415(d));

%o A300253(n) = gcd(A003415(n), A300251(n));

%Y Cf. A003415, A085731, A300245, A300251, A300252.

%K nonn

%O 1,8

%A _Antti Karttunen_, Mar 08 2018

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)