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A307864 a(n) is the number of natural bases b < 2n+1 such that b^n == 1 (mod 2n+1).

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%I A307864 #15 Jul 02 2019 13:39:47
%S A307864 0,1,2,3,2,5,6,1,8,9,4,11,4,1,14,15,4,1,18,1,20,21,4,23,6,1,26,1,4,29,
%T A307864 30,1,16,33,4,35,36,1,4,39,2,41,4,1,44,9,4,1,48,1,50,51,16,53,54,1,56,
%U A307864 1,4,1,10,1,2,63,4,65,36,1,68,69,4,1,16,1,74,75,8,1,78,1,4,81,8,83,12,1,86
%N A307864 a(n) is the number of natural bases b < 2n+1 such that b^n == 1 (mod 2n+1).
%C A307864 For n > 0, a(n) = n if and only if 2n+1 is prime.
%C A307864 If a(n) < n, then 2n+1 is composite.
%C A307864 Theorem: a(n) > n if and only if 2n+1 is an absolute Euler pseudoprime.
%C A307864 Conjecture: if 2n+1 is an absolute Euler pseudoprime, then a(n) = phi(2n+1).
%t A307864 a[n_] := Length[Select[Range[2n], PowerMod[#, n, 2n+1] == 1 &]]; Array[a, 100] (* _Amiram Eldar_, May 02 2019 *)
%o A307864 (PARI) a(n) = sum(b=1, 2*n, Mod(b, 2*n+1)^n == 1); \\ _Michel Marcus_, May 02 2019
%Y A307864 Cf. A000010, A033181, A306530, A307865.
%K A307864 nonn
%O A307864 0,3
%A A307864 _Thomas Ordowski_, May 02 2019
%E A307864 More terms from _Amiram Eldar_, May 02 2019