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A113175 Replace each prime p in prime-factorization of n with p-th Fibonacci number. 4
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
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
Sequence in context: A337943 A275213 A113176 * A109191 A087123 A097131
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 March 3 15:08 EST 2024. Contains 370512 sequences. (Running on oeis4.)