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Number of prime factors, with multiplicity, of Bell number A000110(n).
1

%I #17 Nov 23 2019 04:04:44

%S 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,

%T 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,

%U 5,4,4,10,9,6,6,5,8,5,5,8,5,4,5,3,2

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

%C 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.

%H Amiram Eldar, <a href="/A113908/b113908.txt">Table of n, a(n) for n = 0..104</a>

%H John Sokol, <a href="http://www.dnull.com/bells/bell1000.html">The First 1000 Bell Numbers</a>.

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

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

%p 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

%t Table[PrimeOmega[BellB[n]], {n, 0, 50}] (* _Amiram Eldar_, Nov 23 2019 *)

%Y Cf. A000110, A001222, A113015, A113883.

%K nonn

%O 0,5

%A _Jonathan Vos Post_, Jan 29 2006