

A063684


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


0



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
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OFFSET

1,1


COMMENTS

Equivalently, n such that m(n!) = 2, where m(n) = mu(n+1) + mu(n+2), as mu(n!)=0 for all n>=4 (because 4=2^2 divides n!).  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.


EXAMPLE

8! = 40320, mu(40320) = 0, mu(40321) = 1, mu(40322) = 1, which gives 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 0405 2011
One more term, 114, from Sean A. Irvine, May 25 2015


STATUS

approved



