A216734 - OEIS

A216734

Primes p such that x^6 = -2 has no solution mod p.

5, 7, 13, 19, 23, 29, 31, 37, 47, 53, 61, 67, 71, 73, 79, 97, 101, 103, 109, 127, 139, 149, 151, 157, 163, 167, 173, 181, 191, 193, 197, 199, 211, 223, 229, 239, 241, 263, 269, 271, 277, 293, 311, 313, 317, 331, 337, 349, 359, 367, 373, 379, 383, 389, 397, 409

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OFFSET

1,1

COMMENTS

Complement of A051072 relative to A000040.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

MATHEMATICA

ok[p_] := Reduce[Mod[x^6 + 2, p] == 0, x, Integers] == False; Select[Prime[Range[100]], ok]

PROG

(Magma) [p: p in PrimesUpTo(500) | forall{x: x in ResidueClassRing(p) | x^6 ne -2}]; // Bruno Berselli, Sep 20 2012

(PARI) select(x->!ispower(Mod(-2, x), 6), primes(100)) \\ Michel Marcus, Mar 19 2023