A066856 a(n) = omega(n!+1), where omega is the number of distinct primes dividing n, A001221.

1, 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 3, 5, 3, 6, 2, 2, 3, 3, 3, 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

Offset

1,6

Comments

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 09 2003

Links

Amiram Eldar, Table of n, a(n) for n = 1..139

William Gerst, A conjecture on the prime factorization of n!+1, arXiv:1809.07360 [math.GM], 2018.

Paul Leyland, Factors of n!+1 [Typo in URL corrected by R. J. Mathar, Nov 21 2008]

Hisanori Mishima, Appendix 1. Factorization results for n!+1

Hisanori Mishima, Bernoulli numbers (n = 2 to 114)

Mathematica

Table[ Length[ FactorInteger[ n! + 1]], {n, 1, 15}]

Prog

(PARI) for(n=1, 64, print1(omega(n!+1), ", "))
(Magma) [#PrimeDivisors(Factorial(n) + 1): n in [1..55]]; // Vincenzo Librandi, Oct 11 2018

Crossrefs

Cf. A054990 (bigomega(n!+1)), A002981 (n!+1 is prime), A064237 (n!+1 divisible by a square), A084846 (mu(n!+1)).

Sequence in context: A349954 A081771 A338170 * A089280 A246960 A285200

Adjacent sequences: A066853 A066854 A066855 * A066857 A066858 A066859

Keyword

hard,nonn

Author

Robert G. Wilson v, Jan 21 2002

Extensions

More terms from Rick L. Shepherd, Jun 09 2003

Status

approved