A351121 Numbers k such that k^2 - k + 1 is not squarefree.

19, 23, 31, 68, 69, 80, 117, 129, 147, 166, 178, 192, 215, 227, 264, 276, 293, 313, 314, 316, 325, 361, 362, 374, 411, 423, 424, 430, 440, 460, 472, 485, 500, 509, 521, 522, 530, 558, 570, 582, 607, 619, 654, 656, 668, 699, 700, 705, 711, 717, 754, 766, 788, 791, 803, 815, 823, 852, 864, 868, 901

Offset

1,1

Comments

Numbers k such that, for some prime p == 1 (mod 6), 2*k-1 is a square root of -3 (mod p^2).

Links

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

Example

a(3) = 31 is a term because 31^2 - 31 + 1 = 931 is divisible by 7^2.

Maple

remove(t -> numtheory:-issqrfree(t^2-t+1), [$1..1000]);

Mathematica

Select[Range[1000], ! SquareFreeQ[#^2 - # + 1] &] (* Amiram Eldar, Feb 02 2022 *)

Prog

(PARI) isok(k) = !issquarefree(k^2 - k + 1); \\ Michel Marcus, Feb 02 2022

Crossrefs

Cf. A002061, A005117.

Sequence in context: A261311 A168144 A108271 * A245585 A343741 A060269

Adjacent sequences: A351118 A351119 A351120 * A351122 A351123 A351124

Keyword

nonn

Author

Robert Israel, Feb 01 2022

Status

approved