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 A054990 Number of prime divisors of n! + 1 (counted with multiplicity). 11

%I

%S 1,1,1,2,2,2,2,2,3,2,1,3,2,2,3,5,3,6,2,2,3,3,4,2,2,2,1,2,3,5,4,4,5,2,

%T 5,6,1,2,4,7,1,3,4,3,3,3,4,2,5,5,6,4,4,2,2,4,3,4,2,4,4,3,5,3,4,5,4,5,

%U 6,5,2,7,1,4,2,3,1,6,3,4,7,3,3,3,5,5,4,3,8,3,6,2,4,3,4,5,6,6,5,5,4,5

%N Number of prime divisors of n! + 1 (counted with multiplicity).

%C The smallest k! with n prime factors occurs for n in A060250.

%C 103!+1 = 27437*31084943*C153, so a(103) is unknown until this 153-digit composite is factored. a(104) = 4 and a(105) = 6. - _Rick L. Shepherd_, Jun 10 2003

%H Amiram Eldar, <a href="/A054990/b054990.txt">Table of n, a(n) for n = 1..139</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha103.htm">Factorizations of many number sequences</a>

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha104.htm">Factorizations of many number sequences</a>

%H R. G. Wilson v, <a href="/A038507/a038507.txt">Explicit factorizations</a>

%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/factors/factorial+">Factors of n!+1</a>.

%e a(2)=2 because 4! + 1 = 25 = 5*5

%t a[q_] := Module[{x, n}, x=FactorInteger[q!+1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]

%t A054990[n_Integer] := PrimeOmega[n! + 1]; Table[A054990[n], {n,100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2011 *)

%o (PARI) for(n=1,64,print1(bigomega(n!+1),","))

%Y Cf. A000040 (prime numbers), A001359 (twin primes). Also A054988, A054989, A054991, A054992.

%Y Cf. A066856 (number of distinct prime divisors of n!+1), A084846 (mu(n!+1)).

%K nonn,hard

%O 1,4

%A Arne Ring (arne.ring(AT)epost.de), May 30 2000

%E More terms from _Robert G. Wilson v_, Mar 23 2001

%E More terms from _Rick L. Shepherd_, Jun 10 2003

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Last modified February 23 06:13 EST 2020. Contains 332159 sequences. (Running on oeis4.)