A055228 a(n) = ceiling(sqrt(n!)).

1, 1, 2, 3, 5, 11, 27, 71, 201, 603, 1905, 6318, 21887, 78912, 295260, 1143536, 4574144, 18859678, 80014835, 348776577, 1559776269, 7147792819, 33526120083, 160785623546, 787685471323, 3938427356615, 20082117944246, 104349745809074, 552166953567229

Offset: 0

Author

Henry Bottomley, Jun 21 2000

Keywords

• easy
• nonn

Comments

For n>0, a(n) is the least m>0 such that n! <= m^2. - Clark Kimberling, Jul 18 2012

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..807 (n = 0..300 from T. D. Noe)
• M. Axenovich, D. Fon-Der-Flaass and A. Kostochka, On set systems without weak 3-Delta-subsystems, Discrete Math. 138(1995), 57-62.
• Bela Bollobas, To Prove and Conjecture: Paul Erdős and His Mathematics, Am. Math. Monthly, 105 (March 1998)3, p. 232.
• P. Erdős and R. Rado, Intersection theorems for systems of finite sets I, J. London Math. Soc. (2) 35(1960), 85-90.
• P. Erdős and R. Rado, Intersection theorems for systems of finite sets II, J. London Math. Soc. (2) 44(1969), 467-479.

Crossrefs

Cf. A000142, A003059.

Programs

Maple

A055228:=n->ceil(sqrt(n!)); seq(A055228(n), n=0..30); # Wesley Ivan Hurt, May 06 2014

Mathematica

Table[Ceiling[Sqrt[n!]], {n, 0, 30}] (* Wesley Ivan Hurt, May 06 2014 *)

PARI

a(n) = ceil(sqrt(n!)) \\ Michel Marcus, Jul 30 2013

Python

from math import isqrt, factorial
def A055228(n): return 1+isqrt(factorial(n)-1) # Chai Wah Wu, Jul 28 2022

Formula

a(n) = A003059(A000142(n)). - Jonathan Vos Post, Apr 29 2007

Extensions

A comment stating that one of the terms was wrong has been deleted - the terms are correct. - T. D. Noe, Apr 22 2009

More terms from Wesley Ivan Hurt, May 06 2014