A328845 The first Fibonacci based variant of arithmetic derivative: a(p) = A000045(p) for prime p, a(u*v) = a(u)*v + u*a(v), with a(0) = a(1) = 0.

0, 0, 1, 2, 4, 5, 7, 13, 12, 12, 15, 89, 20, 233, 33, 25, 32, 1597, 33, 4181, 40, 53, 189, 28657, 52, 50, 479, 54, 80, 514229, 65, 1346269, 80, 289, 3211, 100, 84, 24157817, 8381, 725, 100, 165580141, 127, 433494437, 400, 105, 57337, 2971215073, 128, 182, 125, 4825, 984, 53316291173, 135, 500, 188, 12581, 1028487, 956722026041, 160

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..1001

Formula

a(n) = n * Sum e_j * A000045(p_j)/p_j for n = Product p_j^e_j.

a(A000040(n)) = A030426(n).

A007895(a(n)) = A328847(n).

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]));

Crossrefs

Cf. A000040, A000045, A007895, A030426, A113175, A328847.

Cf. also A003415, A258851, A328768, A328769, A328846.

Sequence in context: A116432 A050027 A123643 * A240842 A168540 A115008

Adjacent sequences: A328842 A328843 A328844 * A328846 A328847 A328848

Keyword

nonn

Author

Antti Karttunen, Oct 28 2019

Status

approved