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 A038202 Least k such that n! + k^2 is a square. 9
 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, 337082683248, 163425485250, 8376514506360, 8440230839040, 5088099594240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,3 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(n). - T. D. Noe, Nov 02 2004 For greatest k such that n! + k^2 is a square see A181892; for numbers x such that n! + k^2 = x^2 see A181896. - Artur Jasinski, Mar 31 2012 LINKS Sudipta Mallick, Table of n, a(n) for n = 4..58 Eric Weisstein's World of Mathematics, Brocard's Problem MATHEMATICA Table[f=n!/4; x=Max[Select[Divisors[f], #<=Sqrt[f]&]]; f/x-x, {n, 4, 20}] (* T. D. Noe, Nov 02 2004 *) PROG (PARI) a(n) = my(k=0); while(!issquare(n!+k^2), k++); k; \\ Michel Marcus, Sep 16 2018 CROSSREFS Cf. A038548 (number of divisors of n that are at most sqrt(n)), A068869. Cf. A181892, A181896. Sequence in context: A225118 A273464 A105951 * A128415 A227795 A090479 Adjacent sequences:  A038199 A038200 A038201 * A038203 A038204 A038205 KEYWORD nonn AUTHOR EXTENSIONS a(30)-a(34) from Jon E. Schoenfield, Sep 15 2018 STATUS approved

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Last modified September 17 10:52 EDT 2019. Contains 327129 sequences. (Running on oeis4.)