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%I #15 Feb 02 2022 15:08:23
%S 19,23,31,68,69,80,117,129,147,166,178,192,215,227,264,276,293,313,
%T 314,316,325,361,362,374,411,423,424,430,440,460,472,485,500,509,521,
%U 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
%N Numbers k such that k^2 - k + 1 is not squarefree.
%C Numbers k such that, for some prime p == 1 (mod 6), 2*k-1 is a square root of -3 (mod p^2).
%H Robert Israel, <a href="/A351121/b351121.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 31 is a term because 31^2 - 31 + 1 = 931 is divisible by 7^2.
%p remove(t -> numtheory:-issqrfree(t^2-t+1), [$1..1000]);
%t Select[Range[1000], ! SquareFreeQ[#^2 - # + 1] &] (* _Amiram Eldar_, Feb 02 2022 *)
%o (PARI) isok(k) = !issquarefree(k^2 - k + 1); \\ _Michel Marcus_, Feb 02 2022
%Y Cf. A002061, A005117.
%K nonn
%O 1,1
%A _Robert Israel_, Feb 01 2022
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