

A038202


Least k such that n! + k^2 is a square.


10



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 f1. 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/xx, {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

David W. Wilson


EXTENSIONS

a(30)a(34) from Jon E. Schoenfield, Sep 15 2018


STATUS

approved



