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 A063684 Numbers k such that m(k!) = 2, where m(k) = mu(k) + mu(k+1) + mu(k+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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 14 13:17 EDT 2024. Contains 371661 sequences. (Running on oeis4.)