A113196 a(n) = F(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 k-th Fibonacci number.

1, 1, 1, 1, 1, 4, 1, 1, 1, 11, 1, 24, 1, 29, 61, 1, 1, 76, 1, 451, 421, 199, 1, 1104, 1, 521, 1, 8149, 1, 83204, 1, 1, 19801, 3571, 141961, 146376, 1, 9349, 135721, 974611, 1, 10304396, 1, 2626999, 6675901, 64079, 1, 2435424, 1, 167761, 6376021, 47140601, 1

Offset

1,6

Comments

Every term of sequence is an integer.

Links

Table of n, a(n) for n=1..53.

Formula

a(n) = F(n)/A113195(n).

Example

12 = 2^2 * 3^1, so a(12) = F(12)/ (F(2^2) * F(3^1)) = 144/(3*2) = 24.

Maple

a:= n-> (F-> F(n)/mul(F(i[1]^i[2]), i=ifactors(n)[2]))(k->(<<0|1>, <1|1>>^k)[1, 2]):
seq(a(n), n=1..53);  # Alois P. Heinz, Feb 02 2025

Mathematica

b[t_]:=Fibonacci[First[t]^Last[t]] a[n_]:=Fibonacci[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(fibonacci(n)/p, ", ")) } \\ Lambert Klasen, Oct 26 2005

Crossrefs

Cf. A000045, A113195.

Sequence in context: A222639 A184729 A127707 * A037291 A222317 A063851

Adjacent sequences: A113193 A113194 A113195 * A113197 A113198 A113199

Keyword

nonn

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