A063684 Numbers k such that m(k!) = 2, where m(k) = mu(k) + mu(k+1) + mu(k+2).

8, 13, 14, 18, 19, 20, 25, 36, 38, 43, 48, 51, 52, 54, 60, 71, 74, 75, 78, 80, 87, 91, 92, 105, 108, 110, 112, 114

Offset: 1

Author

Jason Earls, Aug 22 2001

Keywords

• more
• nonn

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

Examples

			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
		

Links

• Dario A. Alpern, Factorization using the Elliptic Curve Method.
• Paul Leyland, Factors of n!+1 (updated 1 Oct 2006).

Crossrefs

Cf. A063838, A008683.

Cf. A084846 (mu(n!+1)).

Programs

PARI

m(n) = moebius(n)+moebius(n+1)+moebius(n+2); for(n=1,10^4, if(m(n!)==2,print(n)))

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