A116370 Number of distinct prime factors of P(L(n)) where L(n) is the Lucas number and P(n) is the unrestricted partition number.

1, 1, 2, 2, 3, 3, 4, 2, 2, 3, 4, 5, 4, 4, 5, 5, 8, 10, 6, 7

Offset

2,3

Links

Table of n, a(n) for n=2..21.

Example

P(L(14)) = 37285884524590579748861394570 = 2 * 3^2 * 5 * 414287605828784219431793273, so the 13th number in the sequence is 4.

Maple

A000041 := proc(n) combinat[numbpart](n) ; end: A000204 := proc(n) option remember ; if n = 1 then 1; elif n = 2 then 3 ; else A000204(n-1)+A000204(n-2) ; fi ; end: A116370 := proc(n) local fcts ; fcts := A000041(A000204(n)) ; nops(numtheory[factorset](fcts)) ; end: for n from 2 to 20 do print(A116370(n)) ; od: # R. J. Mathar, Jan 30 2008

Mathematica

PrimeNu[PartitionsP[LucasL[Range[2, 21]]]] (* Harvey P. Dale, Apr 07 2018 *)

Crossrefs

Sequence in context: A367315 A085561 A260651 * A378160 A261018 A339970

Adjacent sequences: A116367 A116368 A116369 * A116371 A116372 A116373

Keyword

more,nonn

Author

Parthasarathy Nambi, Mar 15 2006

Extensions

2 more terms from R. J. Mathar, Jan 30 2008

a(17)-a(21) from Donovan Johnson, Aug 31 2008

Status

approved