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A054990 Number of prime divisors of n! + 1 (counted with multiplicity). 11
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
The smallest k! with n prime factors occurs for n in A060250.
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
LINKS
R. G. Wilson v, Explicit factorizations
Paul Leyland, Factors of n!+1.
EXAMPLE
a(2)=2 because 4! + 1 = 25 = 5*5
MATHEMATICA
a[q_] := Module[{x, n}, x=FactorInteger[q!+1]; n=Length[x]; Sum[Table[x[[i]][[2]], {i, n}][[j]], {j, n}]]
A054990[n_Integer] := PrimeOmega[n! + 1]; Table[A054990[n], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *)
PROG
(PARI) for(n=1, 64, print1(bigomega(n!+1), ", "))
CROSSREFS
Cf. A000040 (prime numbers), A001359 (twin primes).
Cf. A066856 (number of distinct prime divisors of n!+1), A084846 (mu(n!+1)).
Sequence in context: A330956 A190617 A068323 * A046921 A262954 A262813
KEYWORD
nonn,hard
AUTHOR
Arne Ring (arne.ring(AT)epost.de), May 30 2000
EXTENSIONS
More terms from Robert G. Wilson v, Mar 23 2001
More terms from Rick L. Shepherd, Jun 10 2003
STATUS
approved

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Last modified March 28 04:55 EDT 2024. Contains 371235 sequences. (Running on oeis4.)