A374035 a(n) = gcd(A328845(n), A328846(n)), where A328845 and A328846 are the first and second Fibonacci-based variants of the arithmetic derivative.

0, 0, 1, 1, 4, 5, 1, 1, 12, 6, 5, 1, 4, 1, 3, 5, 32, 1, 3, 1, 20, 1, 3, 1, 4, 50, 1, 27, 8, 1, 5, 1, 80, 1, 1, 25, 12, 1, 1, 1, 20, 1, 1, 1, 20, 15, 7, 1, 16, 14, 25, 1, 4, 1, 27, 20, 4, 1, 1, 1, 80, 1, 33, 3, 192, 10, 1, 1, 8, 1, 5, 1, 12, 1, 1, 25, 12, 1, 1, 1, 80, 108, 1, 1, 4, 15, 1, 1, 4, 1, 15, 1, 60, 1, 1, 10, 16

Offset: 0

Author

Antti Karttunen, Jun 28 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..75025
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A328845, A328846.

Cf. A374036, A374037 (indices of even terms), A374038 (of odd terms).

Programs

PARI

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]));
A328846(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(2+primepi(f[i,1]))/f[i, 1]));
A374035(n) = gcd(A328845(n),A328846(n));

Formula

For all n>= 0, a(5*n) == 0 (mod 5). [There are multiples of 5 at other positions also]