A113908 Number of prime factors, with multiplicity, of Bell number A000110(n).

0, 0, 1, 1, 2, 3, 2, 1, 6, 4, 3, 4, 3, 1, 3, 3, 2, 7, 3, 4, 6, 4, 6, 4, 3, 6, 5, 6, 4, 6, 6, 2, 5, 2, 4, 7, 4, 3, 4, 3, 3, 6, 1, 7, 6, 5, 4, 8, 4, 2, 5, 3, 5, 6, 3, 1, 12, 3, 3, 5, 3, 7, 3, 7, 4, 5, 6, 3, 5, 4, 4, 10, 9, 6, 6, 5, 8, 5, 5, 8, 5, 4, 5, 3, 2

Offset: 0

Author

Jonathan Vos Post, Jan 29 2006

Keywords

• nonn

Comments

This is 1 for A051330 (indices of prime Bell numbers) and is 2 for A113883 (indices of semiprime Bell numbers). The records begin a(0) = 0, a(2) = 1, a(4) = 2, a(5) = 3, a(8) = 6, a(17) = 7, a(56) = 12.

Examples

			a(5) = BigOmega(Bell(5)) = A001222(52) = A001222(2^2 * 13) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..104
• John Sokol, The First 1000 Bell Numbers.

Crossrefs

Cf. A000110, A001222, A113015, A113883.

Programs

Maple

with(numtheory):with(combinat):a:=proc(n) if n=0 then 0 else bigomega(bell(n)) fi end: seq(a(n), n=0..43); # Zerinvary Lajos, Apr 11 2008

Mathematica

Table[PrimeOmega[BellB[n]], {n, 0, 50}] (* Amiram Eldar, Nov 23 2019 *)

Formula

a(n) = BigOmega(A000110(n)). a(n) = A001222(A000110(n)).