A216506 - OEIS

%I #25 May 17 2024 03:22:13

%S 1,2,1,2,1,4,2,2,1,2,1,4,2,2,1,644,1,5700,2,2,1,2,3,4,2,4,1,2,1,12,8,

%T 2,3,2,1,4,5,2,1,2,1,4,2,4,1,14,2,4,2,2,1,2,2,16,2,4,1,12,1,16,273,2,

%U 3,2,1,4,2,2,1,246,1,4,2,2,16,8,1,4,15,2,1,2,4,12

%N Least number k such that k*n+1 is a prime dividing n^(2n) - 1.

%C The corresponding prime factors of n^(2n)-1 of the form k*n+1 is in A216487.

%H Amiram Eldar, <a href="/A216506/b216506.txt">Table of n, a(n) for n = 2..670</a>

%e a(7) = 4 because 7^14 - 1 = 2 ^ 4 * 3 * 29 * 113 * 911 * 4733 and the smallest prime divisor of the form k*n+1 is 29 = 4*7+1 => k = 4.

%t Table[p=First/@FactorInteger[n^(2*n)-1]; (Select[p, Mod[#1, n] == 1 &, 1][[1]]-1)/n, {n, 2, 50}]

%t a[n_] := Module[{m = n + 1}, While[!PrimeQ[m] || PowerMod[n, 2*n, m] != 1, m += n]; (m - 1)/n]; Array[a, 100, 2] (* _Amiram Eldar_, May 17 2024 *)

%o (PARI) a(n) = {my(m = n + 1); while(!isprime(m) || Mod(n, m)^(2*n) != 1, m += n); (m - 1)/n;} \\ _Amiram Eldar_, May 17 2024

%Y Cf. A006486, A007571, A187022, A187023, A216487.

%K nonn

%O 2,2

%A _Michel Lagneau_, Sep 11 2012

%E Data corrected and extended by _Amiram Eldar_, May 17 2024