A113175 Replace each prime p in prime-factorization of n with p-th Fibonacci number.

1, 1, 2, 1, 5, 2, 13, 1, 4, 5, 89, 2, 233, 13, 10, 1, 1597, 4, 4181, 5, 26, 89, 28657, 2, 25, 233, 8, 13, 514229, 10, 1346269, 1, 178, 1597, 65, 4, 24157817, 4181, 466, 5, 165580141, 26, 433494437, 89, 20, 28657, 2971215073, 2, 169, 25, 3194, 233

Offset: 1

Author

Leroy Quet, Oct 16 2005

Keywords

• mult
• nonn
• easy

Comments

If, for p = prime, p^(m_{n,p}) is highest power of p dividing n, m = nonnegative integer, then a(n) is product over all primes of F(p)^(m_{n,p}), where F(p) = p-th Fibonacci number (A000045).

Examples

			63 = 3^2 * 7^1. So a(63) = F(3)^2 * F(7)^1 = 4 * 13 = 52.
		

Links

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

Crossrefs

Cf. A113176, A000045.

Programs

Maple

a:= n-> mul(combinat[fibonacci](i[1])^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..52);  # Alois P. Heinz, Jan 14 2025

Mathematica

Times@@@Table[Fibonacci[#[[1]]]^#[[2]]&/@FactorInteger[n],{n,60}] (* Harvey P. Dale, Mar 30 2024 *)

Sage

[1]+[prod([fibonacci(x[0])^x[1] for x in factor(n)]) for n in range(2,53)] # Danny Rorabaugh, Apr 03 2015

Formula

Totally multiplicative with a(p) = F(p). - Franklin T. Adams-Watters, Jun 05 2006

Extensions

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

Previous Mathematica program deleted by Harvey P. Dale, Mar 30 2024