%I #11 Apr 07 2018 09:59:15
%S 1,1,2,2,3,3,4,2,2,3,4,5,4,4,5,5,8,10,6,7
%N Number of distinct prime factors of P(L(n)) where L(n) is the Lucas number and P(n) is the unrestricted partition number.
%e P(L(14)) = 37285884524590579748861394570 = 2 * 3^2 * 5 * 414287605828784219431793273, so the 13th number in the sequence is 4.
%p 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
%t PrimeNu[PartitionsP[LucasL[Range[2,21]]]] (* _Harvey P. Dale_, Apr 07 2018 *)
%K more,nonn
%O 2,3
%A _Parthasarathy Nambi_, Mar 15 2006
%E 2 more terms from _R. J. Mathar_, Jan 30 2008
%E a(17)-a(21) from _Donovan Johnson_, Aug 31 2008