This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063684 #51 Jul 08 2023 20:14:41 %S A063684 8,13,14,18,19,20,25,36,38,43,48,51,52,54,60,71,74,75,78,80,87,91,92, %T A063684 105,108,110,112,114 %N A063684 Numbers k such that m(k!) = 2, where m(k) = mu(k) + mu(k+1) + mu(k+2). %C A063684 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 %C A063684 127 belongs to the sequence. - _Serge Batalov_, Feb 17 2011 %H A063684 Dario A. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>. %H A063684 Paul Leyland, <a href="https://web.archive.org/web/20191208132430/http://www.leyland.vispa.com:80/numth/factorization/factors/factorial+.txt">Factors of n!+1</a> (updated 1 Oct 2006). %e A063684 8 is a term: 8! = 40320; mu(40320) = 0, mu(40321) = 1, mu(40322) = 1, 0+1+1 = 2. %e A063684 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 A063684 (PARI) m(n) = moebius(n)+moebius(n+1)+moebius(n+2); for(n=1,10^4, if(m(n!)==2,print(n))) %Y A063684 Cf. A063838, A008683. %Y A063684 Cf. A084846 (mu(n!+1)). %K A063684 more,nonn %O A063684 1,1 %A A063684 _Jason Earls_, Aug 22 2001 %E A063684 More terms from _Rick L. Shepherd_, Aug 20 2003 %E A063684 Two more terms from _Sean A. Irvine_, Feb 03 2010, Feb 08 2010 %E A063684 Two new terms, 105 and 108, from _Daniel M. Jensen_, Feb 19 2011, Mar 02 2011 %E A063684 Two more terms, 110 and 112, from _Serge Batalov_, Mar 04-05 2011 %E A063684 One more term, 114, from _Sean A. Irvine_, May 25 2015