A055227 Nearest integer to sqrt( n! ).

1, 1, 1, 2, 5, 11, 27, 71, 201, 602, 1905, 6318, 21886, 78911, 295260, 1143536, 4574144, 18859677, 80014834, 348776577, 1559776269, 7147792818, 33526120082, 160785623545, 787685471323, 3938427356615, 20082117944246, 104349745809074, 552166953567228

Offset: 0

Author

Henry Bottomley, Jun 21 2000

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A000142, A000194, A260373.

Programs

Mathematica

Round[Sqrt[Range[0,30]!]] (* Harvey P. Dale, Aug 27 2013 *)

Python

from gmpy2 import isqrt
A055227_list, g = [1], 1
for i in range(1, 101):
    g *= i
    s = isqrt(g)
    A055227_list.append(int(s if g-s*(s+1) <= 0 else s+1))  # Chai Wah Wu, Jul 24 2015

Formula

a(n) = A000194(A000142(n)).