A083341 Smaller factor of the n-th semiprime of the form (m!)^2 + 1.

13, 101, 17, 101, 1344169, 149, 9049, 37, 710341, 2122590346576634509, 171707860473207588349837, 7686544942807799800864250520468090636146175134909, 2196283505473, 598350346949, 1211221552894876996541369232623365900407018851538797

Offset

1,1

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..17

Andrew Walker, Table of factors of (n!)^2+1.

Formula

Numbers p such that p*q = (A083340(n)!)^2 + 1, p, q prime, p < q.

Example

a(1) = 13 because (A083340(1)!)^2 + 1 = 518401 = 13*39877.
a(15) = 1211221552894876996541369232623365900407018851538797 because (A083340(15)!)^2 + 1 = (55!)^2 + 1 can be factored into P52*P96 with a(15) = P52.

Prog

(PARI) for(n=1, 29, my(f=(n!)^2+1); if(bigomega(f)==2, print1(vecmin(factor(f)[, 1]), ", "))) \\ Hugo Pfoertner, Jul 13 2019

Crossrefs

Cf. A020549, A083340, subsequence of A282706.

Sequence in context: A266002 A367554 A326864 * A336347 A075604 A142297

Adjacent sequences: A083338 A083339 A083340 * A083342 A083343 A083344

Keyword

nonn,hard

Author

Hugo Pfoertner, Apr 25 2003

Extensions

The 11th term of the sequence (49-digit factor of the 100-digit number (41!)^2+1 was found with Yuji Kida's multiple polynomial quadratic sieve UBASIC PPMPQS v3.5 in 13 days CPU time on an Intel PIII 550 MHz.

Missing a(4) and new a(14), a(15) added by Hugo Pfoertner, Jul 13 2019

Status

approved