OFFSET
1,3
COMMENTS
Conjecture: for n>12 and n>0 modulo 12: a(n)=a(n-12) and a(12*k)=A065331(k)*144.
The first part of the conjecture follows from the fact that the Fibonacci numbers are a strong divisibility sequence. - Charles R Greathouse IV, Sep 24 2012
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
Fibonacci(36) = 14930352 = 2^4 * 3^3 * 17 * 19 * 107, therefore a(36) = 2^4 * 3^3 = 432.
MATHEMATICA
a[n_] := Times @@ ({2, 3}^IntegerExponent[Fibonacci[n], {2, 3}]);
Table[a[n], {n, 1, 1000}] (* Jean-François Alcover, Oct 15 2021 *)
PROG
(PARI) fibord(n, p)=if(n==0, return(oo)); my(u=3, t); while((t=((Mod([1, 1; 1, 0], p^u))^n)[1, 2])==0, u*=2); valuation(t, p)
a(n)=if(n%12, return(gcd(fibonacci(n%12), 24))); 3^fibord(n, 3)<<fibord(n, 2) \\ Charles R Greathouse IV, Nov 13 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 20 2003
STATUS
approved