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%I #15 Feb 17 2020 07:15:09
%S 1,1,1,150,1342,2366,1628328,942,9,21,34420,146353232490,3,1,
%T 810589181792,4268555,623525228930150853776330584,1,65647507266341,1,
%U 1,2,15,2,9774000,1,328,75,1,3,44,7,1,2,1,1,3,16353757,2,5036,1,23,23,1,216,1218482865908370401
%N a(n) is the smallest number k such that 2*k*n + 1 is a prime dividing prime(n)^n + 1.
%H Amiram Eldar, <a href="/A191547/b191547.txt">Table of n, a(n) for n = 1..82</a>
%e a(4) = 150 because 2*150*4 + 1 = 1201, which is the smallest prime of the form 2*k*4 + 1 that divides prime(4)^4 + 1 = 7^4 + 1 = 2402 = 2*1201.
%p A191547 :=proc(n) local d,a,k ; a := -1 ; for d in numtheory[factorset](ithprime(n)^n+1) do k := (d-1)/2/n ; if type(k,'integer') and k >0 then if a = -1 then a := k; elif k < a then a := k; end if; end if ; end do: return a ; end proc: # _R. J. Mathar_, Jun 08 2011
%t Table[p=First/@FactorInteger[Prime[ n]^n+1]; (Select[p, Mod[#1, n] == 1 &,
%t 1][[1]] - 1)/(2n), {n, 1, 35}]
%Y Cf. A062006, A191546.
%K nonn
%O 1,4
%A _Michel Lagneau_, Jun 05 2011
%E a(31)-a(46) from _Amiram Eldar_, Feb 17 2020
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