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

Author

Hugo Pfoertner, Mar 25 2003

Keywords

• nonn
• hard

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

Examples

			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).
		

Links

• Dario Alejandro Alpern, Factorization using the Elliptic Curve Method
• Paul Leyland, Factor table Updated 12 May 2007.
• Hisanori Mishima, Factors of n! - 1

Crossrefs

Cf. A078781.

Formula

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

Extensions

a(23) from Hugo Pfoertner, Jul 18 2019

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