

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
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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: A144623 A218975 A048619 * A163281 A307857 A116921
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



