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A063684 Numbers n such that m(n!) = 2, where m(n) = mu(n) + mu(n+1) + mu(n+2). 0

%I

%S 8,13,14,18,19,20,25,36,38,43,48,51,52,54,60,71,74,75,78,80,87,91,92,

%T 105,108,110,112,114

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

%C 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

%C 127 belongs to the sequence. - _Serge Batalov_, Feb 17 2011

%H Dario A. Alpern, <a href="http://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.

%H Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/factors/factorial+.txt">Factors of n!+1</a>.

%e 8! = 40320, mu(40320) = 0, mu(40321) = 1, mu(40322) = 1, which gives 2.

%e 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]

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

%Y Cf. A063838, A008683.

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

%K more,nonn

%O 1,1

%A _Jason Earls_, Aug 22 2001

%E More terms from _Rick L. Shepherd_, Aug 20 2003

%E Two more terms from _Sean A. Irvine_, Feb 03 2010, Feb 08 2010

%E Two new terms, 105 and 108, from _Daniel M. Jensen_, Feb 19 2011, Mar 02 2011

%E Two more terms, 110 and 112, from _Serge Batalov_, Mar 04-05 2011

%E One more term, 114, from _Sean A. Irvine_, May 25 2015

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Last modified June 17 17:12 EDT 2019. Contains 324196 sequences. (Running on oeis4.)