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

0,5

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

Formula

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

Prog

(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));

Crossrefs

Cf. A328845, A328846.

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

Sequence in context: A335862 A200385 A046576 * A016493 A101626 A195853

Adjacent sequences: A374032 A374033 A374034 * A374036 A374037 A374038

Keyword

nonn

Author

Antti Karttunen, Jun 28 2024

Status

approved