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A374116 a(n) = gcd(A328768(n), A328845(n)), where A328768 is the first primorial based variant and A328845 is the first Fibonacci-based variant of the arithmetic derivative, respectively.

%I A374116 #6 Jun 28 2024 21:10:51
%S A374116 0,0,1,2,4,1,7,1,12,12,1,1,20,1,1,1,32,1,33,1,4,1,1,1,52,10,1,54,4,1,
%T A374116 1,1,80,1,1,4,84,1,1,1,4,1,1,1,4,3,1,1,128,14,5,1,4,1,135,4,4,1,1,1,4,
%U A374116 1,1,3,192,6,1,1,4,1,1,1,204,1,1,10,4,2,1,1,16,216,1,1,4,6,1,1,4,1,3,360,4,1,1,24,304,1,7,3,20
%N A374116 a(n) = gcd(A328768(n), A328845(n)), where A328768 is the first primorial based variant and A328845 is the first Fibonacci-based variant of the arithmetic derivative, respectively.
%H A374116 Antti Karttunen, <a href="/A374116/b374116.txt">Table of n, a(n) for n = 0..100000</a>
%o A374116 (PARI)
%o A374116 A002110(n) = prod(i=1,n,prime(i));
%o A374116 A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
%o A374116 A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1]));
%o A374116 A374116(n) = gcd(A328768(n), A328845(n));
%Y A374116 Cf. A328768, A328845.
%Y A374116 Cf. also A374035, A374106.
%K A374116 nonn
%O A374116 0,4
%A A374116 _Antti Karttunen_, Jun 28 2024