A374035 - OEIS

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

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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]));