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%I #14 Feb 17 2020 07:15:29
%S 3,5,7,1201,13421,28393,22796593,15073,163,421,757241,3512477579761,
%T 79,29,24317675453761,136593761,21199857783625129028395239857,37,
%U 2494605276120959,41,43,89,691,97,488700001,53,17713,4201,59,181,2729,449,67,137,71
%N Smallest prime factor of prime(n)^n + 1 having the form 2*k*n+1.
%H Amiram Eldar, <a href="/A191546/b191546.txt">Table of n, a(n) for n = 1..82</a>
%e 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.
%p 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
%t Table[p = First /@ FactorInteger[Prime[n]^n + 1]; Select[p, Mod[#1, n] ==
%t 1 &, 1][[1]], {n, 1, 35}]
%Y Cf. A069463 (Greatest prime factor of prime(n)^n+1).
%K nonn
%O 1,1
%A _Michel Lagneau_, Jun 05 2011
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