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

Author

Vladimir Joseph Stephan Orlovsky, Nov 13 2010

Keywords

• nonn
• more

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

Examples

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

Links

• 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.

Crossrefs

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

Subsequence of A078778.

Programs

Mathematica

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

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