A280420 Product of divisors of n!.

1, 1, 2, 36, 331776, 42998169600000000, 7244150201408990671659859968000000000000000, 1182813011613388022005884215741990164001544397058025540221953280041975323323006976000000000000000000000000000000

Offset: 0

Author

Matthew Campbell, Jan 02 2017

Keywords

• nonn

Links

• Matthew Campbell, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A000005, A000142, A007955, A027423.

Programs

Maple

A280420 := proc(n)
    mul(d,d=numtheory[divisors](n!)) ;
end proc: # R. J. Mathar, Jan 04 2017

Mathematica

Table[(n!)^(DivisorSigma[0, n!]/2), {n, 0, 10}]

Python

from math import isqrt, factorial
from sympy import divisor_count
def A280420(n): return (lambda m:isqrt(m)**c if (c:=divisor_count(m)) & 1 else m**(c//2))(factorial(n)) # Chai Wah Wu, Jun 25 2022

Formula

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

a(n) = (n!)^(d(n!)/2) = (A000142(n))^(A000005(A000142(n))/2).