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

Author

Leroy Quet, Oct 16 2005

Keywords

• nonn
• mult
• easy

Examples

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

Links

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

Crossrefs

Cf. A113175, A000045.

Programs

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 *)

Sage

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

Formula

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

Extensions

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