OFFSET
1,1
COMMENTS
Equivalently, k such that m(k!) = 2, where m(k) = mu(k+1) + mu(k+2), as mu(k!)=0 for all k >= 4 (because 4=2^2 divides k!). - Rick L. Shepherd, Aug 20 2003
127 belongs to the sequence. - Serge Batalov, Feb 17 2011
LINKS
Dario A. Alpern, Factorization using the Elliptic Curve Method.
Paul Leyland, Factors of n!+1 (updated 1 Oct 2006).
EXAMPLE
8 is a term: 8! = 40320; mu(40320) = 0, mu(40321) = 1, mu(40322) = 1, 0+1+1 = 2.
98 is not a term because 98! + 2 = 2 * 31003012014959 * 114951592532951 * 2015644865638913835753087050212028452990938458387 * P78 has an odd number of factors. - Sean A. Irvine, Feb 03 2010
PROG
(PARI) m(n) = moebius(n)+moebius(n+1)+moebius(n+2); for(n=1, 10^4, if(m(n!)==2, print(n)))
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Jason Earls, Aug 22 2001
EXTENSIONS
More terms from Rick L. Shepherd, Aug 20 2003
Two more terms from Sean A. Irvine, Feb 03 2010, Feb 08 2010
Two new terms, 105 and 108, from Daniel M. Jensen, Feb 19 2011, Mar 02 2011
Two more terms, 110 and 112, from Serge Batalov, Mar 04-05 2011
One more term, 114, from Sean A. Irvine, May 25 2015
STATUS
approved