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A280420 Product of divisors of n!. 2
1, 1, 2, 36, 331776, 42998169600000000, 7244150201408990671659859968000000000000000, 1182813011613388022005884215741990164001544397058025540221953280041975323323006976000000000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = A007955(A000142(n)).
a(n) = (n!)^(d(n!)/2) = (A000142(n))^(A000005(A000142(n))/2).
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}]
PROG
(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
CROSSREFS
Sequence in context: A181555 A306644 A283261 * A051459 A358972 A073581
KEYWORD
nonn
AUTHOR
Matthew Campbell, Jan 02 2017
STATUS
approved

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Last modified April 14 14:16 EDT 2024. Contains 371665 sequences. (Running on oeis4.)