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.

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, 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, 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

Offset: 0

Author

Antti Karttunen, Jun 28 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..100000

Crossrefs

Cf. A328768, A328845.

Cf. also A374035, A374106.

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
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]));
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]));
A374116(n) = gcd(A328768(n), A328845(n));