A242830 For p = prime(n), a(n) = number of bases 1 < b < p such that b^(p-1) == 1 (mod p^2).

0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 0, 2, 1, 0, 1, 0, 1, 1, 3, 0, 0, 1, 1, 1, 1, 0, 2, 0, 3, 0, 2, 2, 2, 2, 2, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 0, 4, 0, 1

Offset

1,5

Comments

a(n) > 0 if and only if p is in A134307.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

A242830:= proc(n) local p;
  p:= ithprime(n);
  numboccur(1, [seq(b &^ (p-1) mod p^2, b=2..p-1)]);
end proc;
seq(A242830(n), n=1..1000); # Robert Israel, Jul 16 2014

Mathematica

a[n_] := With[{p = Prime[n]}, Length@Select[Range[2, p-1], PowerMod[#, p-1, p^2] == 1&]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 27 2023 *)

Prog

(PARI) i=0; forprime(p=2, 10^3, a=2; while(a<p, if(Mod(a, p^2)^(p-1)==1, i++); a++); print1(i, ", "); i=0)

Crossrefs

Cf. A001220, A039678, A134307, A185103, A244249.

Sequence in context: A033770 A216283 A262900 * A101668 A141846 A188171

Adjacent sequences: A242827 A242828 A242829 * A242831 A242832 A242833

Keyword

nonn

Author

Felix Fröhlich, Jul 12 2014

Status

approved