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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

%I

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

%N Number of distinct prime factors of P(F(n)) where F(n) is the Fibonacci number and P(n) is the unrestricted partition number.

%F a(n) = A001221(A000041(A000045(n))). - _Michel Marcus_, Jul 31 2015

%e a(14)=3 because F(14)=377 and P(377)=2389 x 16197169 x 41263051.

%p with(combinat): with(numtheory): a:=n->nops(factorset(numbpart(fibonacci(n)))): seq(a(n),n=0..18); # _Emeric Deutsch_, Jul 26 2006

%t Table[PrimeNu[PartitionsP[Fibonacci[n]]], {n, 0, 50}] (* _G. C. Greubel_, May 16 2017 *)

%o (PARI) A116087(n)={ omega(numbpart(fibonacci(n))) ; }

%o { for(n=0,80, print(A116087(n)) ; ) ; } \\ _R. J. Mathar_, Jan 26 2008

%K nonn,more

%O 0,7

%A _Parthasarathy Nambi_, Mar 15 2006

%E More terms from _Emeric Deutsch_, Jul 26 2006

%E More terms from _R. J. Mathar_, Jan 26 2008

%E a(22) from _Amiram Eldar_, Oct 18 2019

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Last modified January 28 07:07 EST 2020. Contains 331317 sequences. (Running on oeis4.)