A181764 Numbers n such that n!+1 is a product of two distinct prime numbers.

6, 8, 10, 13, 14, 19, 20, 24, 25, 26, 28, 34, 38, 48, 54, 55, 59, 71, 75, 92, 109, 114, 115

Offset

1,1

Comments

n! + 1 must be the product of two distinct prime numbers and also the product of only two prime numbers counted with multiplicity. Thus, 12 is NOT a term of the sequence because 12! + 1 = 13*13*2834329. - Harvey P. Dale, Jul 22 2019

Other terms in this sequence: 392, 551, 601, 770, 772, 878, 1033, 1320, 1831, 2620, 2808, 3752, 4233, 4616, 4984, 7260. - Chai Wah Wu, Feb 28 2020

Links

Table of n, a(n) for n=1..23.

Bruce C. Berndt and William F. Galway, On the Brocard-Ramanujan diophantine equation n!+1=m^2, The Ramanujan Journal, March 2000, Volume 4, Issue 1, pp 41-42.

Example

6!+1=7*103; 8!+1=61*661; 10!+1=11*329891; 13!+1=83*75024347; 14!+1=23*3790360487; 19!+1=71*1713311273363831;..

Mathematica

fQ[n_]:=Last/@FactorInteger[n]=={1, 1}; Select[Range[40], fQ[#!+1]&]

Crossrefs

Cf. A033312, A038507, A078781, A085692, A085747, A088332.

Subsequence of A078778.

Sequence in context: A331549 A184111 A330976 * A153032 A086822 A048943

Adjacent sequences: A181761 A181762 A181763 * A181765 A181766 A181767

Keyword

nonn,more

Author

Vladimir Joseph Stephan Orlovsky, Nov 13 2010

Extensions

Extended by D. S. McNeil, Nov 13 2010

One more term (114) (factored by Womack et al.) from Sean A. Irvine, May 25 2015

One more term (115) (factored by Womack et al.) from Sean A. Irvine, Feb 08 2016

Status

approved