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A280420 Product of divisors of n!.

%I A280420 #20 Jun 25 2022 12:54:47
%S A280420 1,1,2,36,331776,42998169600000000,
%T A280420 7244150201408990671659859968000000000000000,
%U A280420 1182813011613388022005884215741990164001544397058025540221953280041975323323006976000000000000000000000000000000
%N A280420 Product of divisors of n!.
%H A280420 Matthew Campbell, <a href="/A280420/b280420.txt">Table of n, a(n) for n = 0..10</a>
%F A280420 a(n) = A007955(A000142(n)).
%F A280420 a(n) = (n!)^(d(n!)/2) = (A000142(n))^(A000005(A000142(n))/2).
%p A280420 A280420 := proc(n)
%p A280420     mul(d,d=numtheory[divisors](n!)) ;
%p A280420 end proc: # _R. J. Mathar_, Jan 04 2017
%t A280420 Table[(n!)^(DivisorSigma[0, n!]/2), {n, 0, 10}]
%o A280420 (Python)
%o A280420 from math import isqrt, factorial
%o A280420 from sympy import divisor_count
%o A280420 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
%Y A280420 Cf. A000005, A000142, A007955, A027423.
%K A280420 nonn
%O A280420 0,3
%A A280420 _Matthew Campbell_, Jan 02 2017