A113176 Product_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the product is over the distinct prime divisors of n.

1, 1, 2, 1, 5, 2, 13, 1, 2, 5, 89, 2, 233, 13, 10, 1, 1597, 2, 4181, 5, 26, 89, 28657, 2, 5, 233, 2, 13, 514229, 10, 1346269, 1, 178, 1597, 65, 2, 24157817, 4181, 466, 5, 165580141, 26, 433494437, 89, 10, 28657, 2971215073, 2, 13, 5, 3194, 233

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = F(p). - Franklin T. Adams-Watters, Jun 05 2006

Example

63 = 3^2 * 7^1. So a(63) = F(3) * F(7) = 2 * 13 = 26.

Mathematica

b[t_]:=Fibonacci[First[t]] a[n_]:=Apply[Times, Map[b, FactorInteger[n]]] (* Esa Peuha, Oct 26 2005 *)
Table[Times@@(Fibonacci[#]&/@FactorInteger[n][[All, 1]]), {n, 60}] (* Harvey P. Dale, May 31 2019 *)

Prog

(Sage) [1]+[prod([fibonacci(p) for p in prime_factors(n)]) for n in range(2, 53)] # Danny Rorabaugh, Apr 03 2015

Crossrefs

Cf. A113175, A000045.

Sequence in context: A341495 A337943 A275213 * A113175 A109191 A087123

Adjacent sequences: A113173 A113174 A113175 * A113177 A113178 A113179

Keyword

nonn,mult,easy

Author

Leroy Quet, Oct 16 2005

Extensions

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

Status

approved