login
A116087
Number of distinct prime factors of P(F(n)) where F(n) is the Fibonacci number and P(n) is the unrestricted partition number.
1
0, 0, 0, 1, 1, 1, 2, 1, 3, 3, 4, 3, 3, 4, 3, 4, 4, 3, 8, 5, 7, 8, 10, 6
OFFSET
0,7
FORMULA
a(n) = A001221(A000041(A000045(n))). - Michel Marcus, Jul 31 2015
EXAMPLE
a(14)=3 because F(14)=377 and P(377)=2389 x 16197169 x 41263051.
MAPLE
with(combinat): with(numtheory): a:=n->nops(factorset(numbpart(fibonacci(n)))): seq(a(n), n=0..18); # Emeric Deutsch, Jul 26 2006
MATHEMATICA
Table[PrimeNu[PartitionsP[Fibonacci[n]]], {n, 0, 50}] (* G. C. Greubel, May 16 2017 *)
PROG
(PARI) A116087(n)={ omega(numbpart(fibonacci(n))) ; }
{ for(n=0, 80, print(A116087(n)) ; ) ; } \\ R. J. Mathar, Jan 26 2008
CROSSREFS
Sequence in context: A340284 A218975 A048619 * A328518 A163281 A307857
KEYWORD
nonn,more
AUTHOR
Parthasarathy Nambi, Mar 15 2006
EXTENSIONS
More terms from Emeric Deutsch, Jul 26 2006
More terms from R. J. Mathar, Jan 26 2008
a(22) from Amiram Eldar, Oct 18 2019
a(23) from Sean A. Irvine, Jun 29 2024
STATUS
approved