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%I #19 Feb 05 2021 03:34:32
%S 1,1,1,2,2,2,5,6,3,2,5,6,7,3,3,4,4,4,5,5,7,6,3,3,5,5,5,6,6,6,6,4,4,5
%N a(n) = omega((prime(n)-1)! + 1), where omega is given by A001221, primes in A000040.
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WilsonsTheorem.html">Wilson's Theorem</a>
%F a(n) = A066856(A006093(n)). - _Jinyuan Wang_, Apr 01 2020
%e a(7) = omega(prime(7)-1)! + 1) = omega((17-1)! + 1) = omega(16! + 1) = omega(2092278988800 + 1) = omega(2092278988801) = 5, as 2092278988801 = 17 * 61 * 137 * 139 * 1059511 = prime(7)*prime(18)*prime(33)*prime(34)*prime(82801).
%t Table[ Length[ FactorInteger[ (Prime[ n ] - 1)! + 1 ] ], {n, 1, 15} ]
%o (PARI) a(n) = omega((prime(n)-1)! + 1); \\ _Jinyuan Wang_, Apr 01 2020
%Y Cf. A000040, A000142, A001221, A006093, A066856.
%K nonn,more
%O 1,4
%A _Reinhard Zumkeller_, Jan 20 2002
%E More terms from _Robert G. Wilson v_, Jan 21 2002
%E a(27)-a(34) from _Jinyuan Wang_, Apr 01 2020
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