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A181764
Numbers n such that n!+1 is a product of two distinct prime numbers.
2
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
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
Subsequence of A078778.
Sequence in context: A331549 A184111 A330976 * A153032 A086822 A048943
KEYWORD
nonn,more
AUTHOR
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