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A308464
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Squarefree numbers of the form m^2 + 4.
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1
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5, 13, 29, 53, 85, 173, 229, 293, 365, 445, 533, 629, 733, 965, 1093, 1229, 1373, 1685, 1853, 2029, 2213, 2405, 2605, 2813, 3029, 3253, 3485, 3973, 4229, 4493, 4765, 5045, 5333, 5629, 5933, 6245, 6565, 6893, 7229, 7573, 8285, 8653, 9029, 9413, 9805
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OFFSET
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1,1
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COMMENTS
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Yokoi's conjecture posits that, except for most of the values less than 365, the ring of algebraic integers of Q(sqrt(a(n)) has class number greater than 1. Only one counterexample to this conjecture may exist, and it would also be a counterexample to the generalized Riemann hypothesis, according to Mollin (1996).
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REFERENCES
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Richard A. Mollin, Quadratics. Boca Raton, Florida: CRC Press (1996): 176 - 177.
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LINKS
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MAPLE
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select(numtheory:-issqrfree, [seq(m^2+4, m=1..1000, 2)]); # Robert Israel, Jun 05 2019
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MATHEMATICA
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Select[(2Range[50] - 1)^2 + 4, MoebiusMu[#] != 0 &]
Select[Table[i^2 + 4, {i, 1, 100}], SquareFreeQ] (* Navvye Anand, Jun 20 2024 *)
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PROG
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(PARI) is(n) = issquarefree(n) && issquare(n-4) \\ Felix Fröhlich, May 29 2019
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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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