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A307864
a(n) is the number of natural bases b < 2n+1 such that b^n == 1 (mod 2n+1).
1
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, 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, 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
OFFSET
0,3
COMMENTS
For n > 0, a(n) = n if and only if 2n+1 is prime.
If a(n) < n, then 2n+1 is composite.
Theorem: a(n) > n if and only if 2n+1 is an absolute Euler pseudoprime.
Conjecture: if 2n+1 is an absolute Euler pseudoprime, then a(n) = phi(2n+1).
MATHEMATICA
a[n_] := Length[Select[Range[2n], PowerMod[#, n, 2n+1] == 1 &]]; Array[a, 100] (* Amiram Eldar, May 02 2019 *)
PROG
(PARI) a(n) = sum(b=1, 2*n, Mod(b, 2*n+1)^n == 1); \\ Michel Marcus, May 02 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, May 02 2019
EXTENSIONS
More terms from Amiram Eldar, May 02 2019
STATUS
approved