A363833 Number of prime factors of A000129(n) (Pell numbers) (counted with multiplicity).

0, 1, 1, 3, 1, 3, 2, 5, 2, 3, 1, 7, 1, 4, 4, 7, 2, 5, 2, 7, 4, 4, 2, 10, 3, 4, 4, 8, 1, 9, 3, 9, 3, 5, 4, 12, 3, 4, 4, 11, 1, 9, 2, 9, 7, 5, 2, 14, 4, 6, 5, 8, 1, 8, 5, 11, 5, 3, 1, 17, 3, 6, 7, 13, 6, 8, 2, 10, 4, 9, 3, 17, 2, 7, 10, 10, 6, 10, 4, 15, 7, 5, 2

Offset: 1

Author

Tyler Busby, Oct 19 2023

Keywords

• nonn

Examples

			a(8)=5 because Pell(8)=408 has prime factors {2, 2, 2, 3, 17}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..630 (calculated using Jon E. Schoenfield's a-file at A000129)

Crossrefs

Cf. A000129, A001222, A272040, A363829, A363831, A364818.

Programs

Mathematica

PrimeOmega[LinearRecurrence[{2,1},{1,2},83]] (* Stefano Spezia, Oct 19 2023 *)

Formula

a(n) = bigomega(Pell(n)) = A001222(A000129(n)).