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 A083340 Numbers n such that A020549(n)=(n!)^2+1 is a semiprime. 2
 6, 7, 8, 12, 15, 16, 17, 18, 19, 28, 29, 41, 45, 53, 55, 61, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The smaller of the two prime factors is given in A083341. The next candidates for a continuation are 55 and 61. (55!)^2 + 1 is composite with 147 decimal digits and unknown factorization. (55!)^2 + 1 has been factored using ECM into P52*P96 with P52 = A083341(15). (61!)^2 + 1 is composite with 168 decimal digits. - Hugo Pfoertner, Jul 13 2019 Using CADO-NFS, (61!)^2 + 1 has been factored into P58*P110 with P58 = A282706(61) in 17 days wall clock time using 56 million CPU seconds. a(18) >= 75. - Hugo Pfoertner, Aug 04 2019 LINKS The CADO-NFS Development Team, CADO-NFS, An Implementation of the Number Field Sieve Algorithm, Release 2.3.0, 2017 Andrew Walker, Factors of (n!)^2+1. factordb.com, Status of 75!^2+1. EXAMPLE a(1)=6 because (6!)^2+1=518401=13*39877 is a semiprime. MATHEMATICA Select[Range[60], PrimeOmega[(#!)^2+1]==2&] (* Harvey P. Dale, Dec 12 2018 *) CROSSREFS Cf. A020549, A001358, A083341, A046029, A282706. Sequence in context: A274556 A066235 A037365 * A118733 A047275 A327301 Adjacent sequences:  A083337 A083338 A083339 * A083341 A083342 A083343 KEYWORD nonn,more,hard AUTHOR Hugo Pfoertner, Apr 24 2003 EXTENSIONS a(15) from Hugo Pfoertner, Jul 13 2019 a(16), a(17) from Hugo Pfoertner, Aug 04 2019 STATUS approved

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Last modified September 17 04:03 EDT 2019. Contains 327119 sequences. (Running on oeis4.)