A080802 Smaller of the two factors of the n-th semiprime number of the form m!-1.

7, 23, 29, 1733, 3041, 124769, 51871, 625793187653, 20431, 29, 10398560889846739639, 155166770881, 9190813196017748117, 340777, 3282689, 61, 895269581, 21289796287569735866708594882309656982337071, 14380211646881467415803462581621417951534002839, 884057, 139, 7533609175373352257, 1712114014849097863989021395568379341467597467171639484099

Offset

1,1

Comments

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).

151!-1 has been factored into P58*P208. - Hugo Pfoertner, Jul 18 2019

Links

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

Dario Alejandro Alpern, Factorization using the Elliptic Curve Method

Paul Leyland, Factor table Updated 12 May 2007.

Hisanori Mishima, Factors of n! - 1

Formula

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

Example

a(1)=7 because A078781(1)!-1=5!-1=7*17,
a(2)=23 because A078781(2)!-1=8!-1=23*1753,
a(11)=10398560889846739639 because A078781(11)!-1=34!-1= 10398560889846739639*28391697867333973241 (20 digits each).

Crossrefs

Cf. A078781.

Sequence in context: A038948 A019389 A056723 * A078515 A225822 A044449

Adjacent sequences: A080799 A080800 A080801 * A080803 A080804 A080805

Keyword

nonn,hard

Author

Hugo Pfoertner, Mar 25 2003

Extensions

a(23) from Hugo Pfoertner, Jul 18 2019

Status

approved