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.
FORMULA
Multiplicative with a(p^e) = F(p^e). - Franklin T. Adams-Watters, Jun 05 2006
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/F(p^k)) = 4.7856032241... . - Amiram Eldar, Jan 20 2024
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]]] (* Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 26 2005 *)
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, ", ")) \\ Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 26 2005
CROSSREFS
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