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%I #13 Apr 03 2023 10:36:10
%S 3,3,2,1,1,1,1,3,3,3,3,2,3,3,4,2,2,3,3,5,5,5,3,4,3,2,4,5,5,4,7,6,4,4,
%T 7,2,5,4,7,4,5,3,4,6,5,4,3,3,5,6,3,5,6,3,3,7,4,5,5,2,4,4,5,4,2,4,3,5,
%U 2,5,7,4,7,5,5,3,5,4,6,6,8,5
%N Number of prime factors in n!+7 (counted with multiplicity).
%D C. Caldwell and H. Dubner, "Primorial, factorial and multifactorial primes," Math. Spectrum, 26:1 (1993/4) 1-7.
%H Chris Caldwell, <a href="https://t5k.org/glossary/page.php?sort=MultifactorialPrime">multifactorial prime (another Prime Pages' Glossary entries)</a>.
%H Ken Davis, <a href="http://mfprimes.free-dc.org">Status of Search for Multifactorial Primes</a>.
%H Sean A. Irvine, <a href="/A100013/a100013.txt">Factorizations of n!+7</a>
%e Example 1!+7 = 2^3 so a(1) = 3.
%e a(3) = a(4) = a(5) = a(6) = 1 because 3!+1 = 13, 4!+7 = 31, 5!+1 = 127, 6!+7 = 727 and these are all primes. a(11) = a(15) = a(16) = a(25) = a(35) = a(59) = 2 because 11!+7 = 39916807 = 7 * 5702401, 15!+7 = 1307674368007 = 7 * 186810624001, 16!+7 = 20922789888007 = 7 * 2988969984001, 25!+7 = 15511210043330985984000007 = 7 * 2215887149047283712000001, 35!+7 = 10333147966386144929666651337523200000007 = 7 *
%e 1476163995198020704238093048217600000001 and 59!+7 = 138683118545689835737939019720389406345902876772687432540821294940160000000000007 = 7 * 19811874077955690819705574245769915192271839538955347505831613562880000000000001 are all semiprimes.
%Y Cf. A002981, A037083, A037083, A085150, A085148, A085146, A062701, A055487, A062702.
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, Nov 18 2004
%E More terms from _Sean A. Irvine_, Sep 20 2012
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