A214078 a(n) = (ceiling (sqrt(n)))!.

1, 1, 2, 2, 2, 6, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120, 120, 120, 120, 120, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 720, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 5040, 40320, 40320, 40320

Offset: 0

Author

Mohammad K. Azarian, Dec 22 2012

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A214078, A214079, A214080, A214081, A214083, A055228, A055226.

Cf. A000142, A003059.

Programs

Derive

PROG(y := [], n := 50, LOOP(IF(n = -1, RETURN y), y := ADJOIN(CEILING(SQRT(n))!, y), n := n - 1))

Magma

[Factorial(Ceiling (Sqrt(n))): n in [0..50]]; // Vincenzo Librandi, Feb 13 2013

Mathematica

Table[Ceiling[Sqrt[n]]!, {n, 0, 50}] (* T. D. Noe, Dec 23 2012 *)

PARI

a(n) = ceil(sqrt(n))!; \\ Altug Alkan, Jan 11 2016

Python

from math import factorial, isqrt
def A214078(n): return factorial(1+isqrt(n-1)) if n else 1 # Chai Wah Wu, Jul 28 2022

Formula

a(n) = A000142(A003059(n)). - Michel Marcus, Jul 28 2022

Sum_{n>=0} 1/a(n) = e + 2. - Amiram Eldar, Aug 15 2022