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A351121
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Numbers k such that k^2 - k + 1 is not squarefree.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Numbers k such that, for some prime p == 1 (mod 6), 2*k-1 is a square root of -3 (mod p^2).
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LINKS
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EXAMPLE
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a(3) = 31 is a term because 31^2 - 31 + 1 = 931 is divisible by 7^2.
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MAPLE
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remove(t -> numtheory:-issqrfree(t^2-t+1), [$1..1000]);
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MATHEMATICA
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Select[Range[1000], ! SquareFreeQ[#^2 - # + 1] &] (* Amiram Eldar, Feb 02 2022 *)
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PROG
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(PARI) isok(k) = !issquarefree(k^2 - k + 1); \\ Michel Marcus, Feb 02 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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