A080802 - OEIS

%I #14 Jul 08 2023 18:09:09

%S 7,23,29,1733,3041,124769,51871,625793187653,20431,29,

%T 10398560889846739639,155166770881,9190813196017748117,340777,3282689,

%U 61,895269581,21289796287569735866708594882309656982337071,14380211646881467415803462581621417951534002839,884057,139,7533609175373352257,1712114014849097863989021395568379341467597467171639484099

%N Smaller of the two factors of the n-th semiprime number of the form m!-1.

%C To continue the sequence the factorizations of 151!-1 and 154!-1 are required, which are composite numbers with 265 and 272 digits, respectively. The next term would then be 37272934189201737869016720929 (factor of 157!-1).

%C 151!-1 has been factored into P58*P208. - _Hugo Pfoertner_, Jul 18 2019

%H Dario Alejandro Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>

%H Paul Leyland, <a href="https://web.archive.org/web/20171111200123/http://www.leyland.vispa.com/numth/factorization/factors/factorial-">Factor table</a> Updated 12 May 2007.

%H Hisanori Mishima, <a href="https://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/factorial-.txt">Factors of n! - 1</a>

%F Numbers p such that p*q=A078781(n)!-1, p, q prime, p<q.

%e a(1)=7 because A078781(1)!-1=5!-1=7*17,

%e a(2)=23 because A078781(2)!-1=8!-1=23*1753,

%e a(11)=10398560889846739639 because A078781(11)!-1=34!-1= 10398560889846739639*28391697867333973241 (20 digits each).

%Y Cf. A078781.

%K nonn,hard

%O 1,1

%A _Hugo Pfoertner_, Mar 25 2003

%E a(23) from _Hugo Pfoertner_, Jul 18 2019