

A113195


a(n) = product{p=primes} F(p^(m_{n,p})), where p^(m_{n,p}) is highest power of p dividing n, m= nonnegative integer and F(k) is the kth Fibonacci number.


2



1, 1, 2, 3, 5, 2, 13, 21, 34, 5, 89, 6, 233, 13, 10, 987, 1597, 34, 4181, 15, 26, 89, 28657, 42, 75025, 233, 196418, 39, 514229, 10, 1346269, 2178309, 178, 1597, 65, 102, 24157817, 4181, 466, 105, 165580141, 26, 433494437, 267, 170, 28657, 2971215073
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OFFSET

1,3


COMMENTS

F(p^j) is always coprime to F(q^k), where p and q are distinct primes and j and k are nonnegative integers.


LINKS

Table of n, a(n) for n=1..47.


FORMULA

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


EXAMPLE

45 = 3^2 * 5^1, so a(45) = F(3^2) * F(5^1) = 34 * 5 = 170.


MATHEMATICA

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


PROG

(PARI) for(n=1, 100, f=factor(n); p=1; for(i=1, matsize(f)[1], p*=fibonacci(f[i, 1]^f[i, 2])); print1(p, ", ")) (Klasen)


CROSSREFS

Cf. A113196.
Sequence in context: A060442 A060385 A080648 * A069110 A238684 A202694
Adjacent sequences: A113192 A113193 A113194 * A113196 A113197 A113198


KEYWORD

nonn,mult


AUTHOR

Leroy Quet, Oct 17 2005


EXTENSIONS

More terms from Esa Peuha (esa.peuha(AT)helsinki.fi) and Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 26 2005


STATUS

approved



