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A083341
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Smaller factor of the n-th semiprime of the form (m!)^2 + 1.
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3
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13, 101, 17, 101, 1344169, 149, 9049, 37, 710341, 2122590346576634509, 171707860473207588349837, 7686544942807799800864250520468090636146175134909, 2196283505473, 598350346949, 1211221552894876996541369232623365900407018851538797
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OFFSET
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1,1
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LINKS
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FORMULA
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Numbers p such that p*q = (A083340(n)!)^2 + 1, p, q prime, p < q.
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EXAMPLE
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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.
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PROG
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(PARI) for(n=1, 29, my(f=(n!)^2+1); if(bigomega(f)==2, print1(vecmin(factor(f)[, 1]), ", "))) \\ Hugo Pfoertner, Jul 13 2019
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CROSSREFS
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KEYWORD
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nonn,hard,changed
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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