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

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));

Crossrefs

Cf. A000040, A000045, A030426, A113177, A328845.

Cf. also A374035.

Sequence in context: A249033 A068762 A326914 * A155679 A319771 A021448

Adjacent sequences: A374102 A374103 A374104 * A374107 A374108 A374109

Keyword

nonn

Author

Antti Karttunen, Jun 28 2024

Status

approved