A184391 a(n) = product of numbers from 1 to A007955(n).

1, 2, 6, 40320, 120, 371993326789901217467999448150835200000000, 5040, 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000, 10888869450418352160768000000

Offset: 1

Author

Jaroslav Krizek, Jan 12 2011

Keywords

• nonn

Links

• Robert P. P. McKone, Table of n, a(n) for n = 1..11

Crossrefs

Cf. A184387, A184388, A184389, A184390, A130674.

Programs

Mathematica

A184391[n_] := Product[i, {i, 1, n^(DivisorSigma[0, n]/2)}]; Table[A184391[n], {n, 1, 9}] (* Robert P. P. McKone, Feb 04 2021 *)

Python

from math import isqrt, factorial
from sympy import divisor_count
def A184391(n): return factorial((isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2)) # Chai Wah Wu, Jun 25 2022

Formula

a(n) = A007955(n)! = A000142(A007955(n)).

Extensions

a(9) from Robert P. P. McKone, Feb 04 2021