A113178 a(n) = Sum_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the sum is over the distinct prime divisors of n.

0, 1, 2, 1, 5, 3, 13, 1, 2, 6, 89, 3, 233, 14, 7, 1, 1597, 3, 4181, 6, 15, 90, 28657, 3, 5, 234, 2, 14, 514229, 8, 1346269, 1, 91, 1598, 18, 3, 24157817, 4182, 235, 6, 165580141, 16, 433494437, 90, 7, 28658, 2971215073, 3, 13, 6, 1599, 234

Offset

1,3

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..4000

Formula

Additive with a(p^e) = F(p).

Example

12 = 2^2 * 3^1, so a(12) = F(2) + F(3) = 1 + 2 = 3.

Mathematica

b[t_]:=Fibonacci[First[t]] a[n_]:=Apply[Plus, Map[b, FactorInteger[n]]] (* Esa Peuha, Oct 26 2005 *)

Prog

(Sage) [0]+[sum([fibonacci(p) for p in prime_factors(n)]) for n in range(2, 53)] # Danny Rorabaugh, Apr 03 2015

Crossrefs

Cf. A000045, A113177.

Sequence in context: A114901 A355562 A194809 * A108362 A171090 A141506

Adjacent sequences: A113175 A113176 A113177 * A113179 A113180 A113181

Keyword

nonn,easy

Author

Leroy Quet, Oct 16 2005

Extensions

More terms from Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 26 2005

Status

approved