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A083341
Smaller factor of the n-th semiprime of the form (m!)^2 + 1.
3
13, 101, 17, 101, 1344169, 149, 9049, 37, 710341, 2122590346576634509, 171707860473207588349837, 7686544942807799800864250520468090636146175134909, 2196283505473, 598350346949, 1211221552894876996541369232623365900407018851538797
OFFSET
1,1
LINKS
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
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