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A191546
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Smallest prime factor of prime(n)^n + 1 having the form 2*k*n+1.
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2
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3, 5, 7, 1201, 13421, 28393, 22796593, 15073, 163, 421, 757241, 3512477579761, 79, 29, 24317675453761, 136593761, 21199857783625129028395239857, 37, 2494605276120959, 41, 43, 89, 691, 97, 488700001, 53, 17713, 4201, 59, 181, 2729, 449, 67, 137, 71
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(4) = 1201 because prime(4)^4 + 1 = 7^4+1 = 2402 = 2*1201; the prime divisor of the form 2kn + 1 is 1201 = 2*150*4 + 1 with k = 150.
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MAPLE
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A191546 := proc(n) local ifs, twkn ; ifs := sort(convert(numtheory[factorset]( 1+ithprime(n)^n), list)) ; for twkn in ifs do if (twkn-1) mod (2*n) = 0 then return twkn; end if; end do: return -1 ; end proc: # R. J. Mathar, Jun 18 2011
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MATHEMATICA
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Table[p = First /@ FactorInteger[Prime[n]^n + 1]; Select[p, Mod[#1, n] ==
1 &, 1][[1]], {n, 1, 35}]
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CROSSREFS
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Cf. A069463 (Greatest prime factor of prime(n)^n+1).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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