A243805 Integers k such that 6 is a 6th power mod k.

1, 2, 3, 5, 6, 10, 15, 23, 25, 29, 30, 46, 47, 50, 53, 58, 69, 71, 75, 87, 94, 101, 106, 115, 125, 138, 139, 141, 142, 145, 149, 150, 159, 163, 167, 173, 174, 191, 197, 202, 213, 230, 235, 239, 241, 250, 263, 265, 269, 278, 282, 290, 293, 298, 303, 307, 311, 313, 317, 318, 326, 334, 337, 345, 346, 355, 359, 375, 379, 382, 383, 389

Offset

1,2

Comments

All n such that there exists at least one integer x with x^6 == 6 mod n.

n is in the sequence iff n is not divisible by 4 or 9 or any member of A243768.

Links

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

Example

5 is in the sequence because 1^6 == 6 mod 5.

Maple

select(n -> nops([msolve(x^6-6, n)])>0, [$1..1000]);

Mathematica

Select[Range[1000], # == 1 || Solve[x^6-6 == 0, x, Modulus -> #] != {}&] (* Jean-François Alcover, Apr 27 2019 *)

Prog

(PARI) isok(n) = ispower(Mod(6, n), 6) ; \\ fails with 2.11.1 but will work with 2.11.2; Michel Marcus, Apr 28 2019

Crossrefs

Cf. A243768 (primes not in this sequence).

Sequence in context: A262931 A018524 A057035 * A018594 A018626 A018305

Adjacent sequences: A243802 A243803 A243804 * A243806 A243807 A243808

Keyword

nonn

Author

Robert Israel, Jun 10 2014

Status

approved