cp's OEIS Frontend

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

%I A066856 #23 Feb 07 2025 05:36:07
%S A066856 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,
%T A066856 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 A066856 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 A066856 a(n) = omega(n!+1), where omega is the number of distinct primes dividing n, A001221.
%C A066856 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
%H A066856 Amiram Eldar, <a href="/A066856/b066856.txt">Table of n, a(n) for n = 1..139</a>
%H A066856 William Gerst, <a href="https://arxiv.org/abs/1809.07360">A conjecture on the prime factorization of n!+1</a>, arXiv:1809.07360 [math.GM], 2018.
%H A066856 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/factors/factorial+.txt">Factors of n!+1</a> [Typo in URL corrected by R. J. Mathar, Nov 21 2008]
%H A066856 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha104.htm">Appendix 1. Factorization results for n!+1</a>
%H A066856 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha134.htm">Bernoulli numbers (n = 2 to 114)</a>
%t A066856 Table[ Length[ FactorInteger[ n! + 1]], {n, 1, 15}]
%t A066856 PrimeNu[Range[50]! + 1] (* _Paolo Xausa_, Feb 07 2025 *)
%o A066856 (PARI) for(n=1,64,print1(omega(n!+1),","))
%o A066856 (Magma) [#PrimeDivisors(Factorial(n) + 1): n in [1..55]]; // _Vincenzo Librandi_, Oct 11 2018
%Y A066856 Cf. A054990 (bigomega(n!+1)), A002981 (n!+1 is prime), A064237 (n!+1 divisible by a square), A084846 (mu(n!+1)).
%K A066856 hard,nonn
%O A066856 1,6
%A A066856 _Robert G. Wilson v_, Jan 21 2002
%E A066856 More terms from _Rick L. Shepherd_, Jun 09 2003