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A113175 Replace each prime p in prime-factorization of n with p-th Fibonacci number. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A113176, A000045.

Sequence in context: A318972 A275213 A113176 * A109191 A087123 A097131

Adjacent sequences:  A113172 A113173 A113174 * A113176 A113177 A113178

KEYWORD

mult,nonn,easy

AUTHOR

Leroy Quet, Oct 16 2005

EXTENSIONS

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

STATUS

approved

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Last modified May 19 02:45 EDT 2019. Contains 323377 sequences. (Running on oeis4.)