A374106 - OEIS

A374106

a(n) = gcd(A113177(n), A328845(n)), where A113177 is fully additive with a(p) = Fibonacci(p) and A328845 is the first Fibonacci-based variant of the arithmetic derivative.

0, 1, 2, 2, 5, 1, 13, 3, 4, 3, 89, 4, 233, 1, 1, 4, 1597, 1, 4181, 1, 1, 9, 28657, 1, 10, 1, 6, 5, 514229, 1, 1346269, 5, 1, 1, 2, 6, 24157817, 17, 5, 4, 165580141, 1, 433494437, 1, 3, 7, 2971215073, 2, 26, 1, 1, 1, 53316291173, 1, 2, 4, 1, 3, 956722026041, 1, 2504730781961, 1, 1, 6, 2, 1, 44945570212853, 3, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4500

FORMULA

For all n >= 1, a(A000040(n)) = A030426(n).

PROG

(PARI)

A113177(n) = if(n<=1, 0, my(f=factor(n)); sum(i=1, #f~, f[i, 2]*fibonacci(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]));

A374106(n) = gcd(A113177(n), A328845(n));