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

1,1

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

Table of n, a(n) for n=1..28.

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

Cf. A063838, A008683.

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

Sequence in context: A124159 A128662 A133192 * A059194 A253775 A168137

Adjacent sequences: A063681 A063682 A063683 * A063685 A063686 A063687

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