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A353887
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Squarefree numbers of the form k^2 + k + 1 for some k >= 0.
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4
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1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133, 157, 183, 211, 241, 273, 307, 381, 421, 463, 553, 601, 651, 703, 757, 813, 871, 993, 1057, 1123, 1191, 1261, 1333, 1407, 1483, 1561, 1641, 1723, 1807, 1893, 1981, 2071, 2163, 2257, 2353, 2451, 2551, 2653, 2757
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OFFSET
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1,2
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COMMENTS
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Dimitrov proved that this sequence is infinite.
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LINKS
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FORMULA
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EXAMPLE
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4^2 + 4 + 1 = 21 = 3 * 7 is squarefree, so 21 belongs to this sequence.
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MATHEMATICA
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Select[Table[n^2 + n + 1, {n, 0, 52}], SquareFreeQ] (* Amiram Eldar, Dec 11 2023 *)
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PROG
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(PARI) for (k=0, 52, if (issquarefree(m=k^2+k+1), print1 (m", ")))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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