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A038202
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Least k such that n!+k^2 is a square.
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1
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1, 1, 3, 1, 9, 27, 15, 18, 288, 288, 420, 464, 1856, 10080, 46848, 210240, 400320, 652848, 3991680, 27528402, 32659200, 163296000, 1143463200, 1305467240, 6840489600, 9453465438
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,3
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COMMENTS
| Let f=n!/4 and let x be the largest divisor of f such that x < sqrt(f). Then a(n) = f/x - x. The greatest k such that n!+k^2 is a square is f-1. The number of k for which n!+k^2 is a square is A038548(f). - T. D. Noe (noe(AT)sspectra.com), Nov 02 2004
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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MATHEMATICA
| Table[f=n!/4; x=Max[Select[Divisors[f], #<=Sqrt[f]&]]; f/x-x, {n, 4, 20}] (T. D. Noe)
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CROSSREFS
| Cf. A038548 (number of divisors of n that are at most sqrt(n)).
Sequence in context: A160568 A157403 A105951 * A128415 A090479 A141903
Adjacent sequences: A038199 A038200 A038201 * A038203 A038204 A038205
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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