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%I #25 Dec 23 2021 00:31:28
%S 13,101,17,101,1344169,149,9049,37,710341,2122590346576634509,
%T 171707860473207588349837,
%U 7686544942807799800864250520468090636146175134909,2196283505473,598350346949,1211221552894876996541369232623365900407018851538797
%N Smaller factor of the n-th semiprime of the form (m!)^2 + 1.
%H Hugo Pfoertner, <a href="/A083341/b083341.txt">Table of n, a(n) for n = 1..17</a>
%H Andrew Walker, <a href="http://web.archive.org/web/20080808141339/http://www.uow.edu.au/~ajw01/ecm/pluspp.txt">Table of factors of (n!)^2+1</a>.
%F Numbers p such that p*q = (A083340(n)!)^2 + 1, p, q prime, p < q.
%e a(1) = 13 because (A083340(1)!)^2 + 1 = 518401 = 13*39877.
%e a(15) = 1211221552894876996541369232623365900407018851538797 because (A083340(15)!)^2 + 1 = (55!)^2 + 1 can be factored into P52*P96 with a(15) = P52.
%o (PARI) for(n=1,29,my(f=(n!)^2+1);if(bigomega(f)==2,print1(vecmin(factor(f)[,1]),", "))) \\ _Hugo Pfoertner_, Jul 13 2019
%Y Cf. A020549, A083340, subsequence of A282706.
%K nonn,hard
%O 1,1
%A _Hugo Pfoertner_, Apr 25 2003
%E 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.
%E Missing a(4) and new a(14), a(15) added by _Hugo Pfoertner_, Jul 13 2019
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