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.

0, 0, 0, 1, 1, 1, 2, 1, 3, 3, 4, 3, 3, 4, 3, 4, 4, 3, 8, 5, 7, 8, 10

Offset

0,7

Links

Table of n, a(n) for n=0..22.

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

Adjacent sequences: A116084 A116085 A116086 * A116088 A116089 A116090

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

Status

approved