|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
