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

0,5

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.

Links

Amiram Eldar, Table of n, a(n) for n = 0..104

John Sokol, The First 1000 Bell Numbers.

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000110, A001222, A113015, A113883.

Sequence in context: A324646 A370180 A286156 * A355624 A065369 A336404

Adjacent sequences: A113905 A113906 A113907 * A113909 A113910 A113911

Keyword

nonn

Author

Jonathan Vos Post, Jan 29 2006

Status

approved