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A175493 a(n) = Product_{k=1..n} k^d(k), where d(k) = number of divisors of k.

%I A175493 #21 May 03 2022 21:16:20
%S A175493 1,4,36,2304,57600,74649600,3657830400,14982473318400,
%T A175493 10922223049113600,109222230491136000000,13215889889427456000000,
%U A175493 39462435755592152776704000000,6669151642695073819262976000000,256202129505773955840806486016000000
%N A175493 a(n) = Product_{k=1..n} k^d(k), where d(k) = number of divisors of k.
%C A175493 a(n) = a(n-1)*A062758(n).
%C A175493 a(n) = Product_{k=1..n} k^floor(n/k) * (floor(n/k))!.
%H A175493 Michael S. Branicky, <a href="/A175493/b175493.txt">Table of n, a(n) for n = 1..117</a>
%t A175493 f[n_] := Product[ k^DivisorSigma[0, k], {k, n}]; Array[f, 15] (* _Robert G. Wilson v_, Jun 11 2010 *)
%o A175493 (Python)
%o A175493 from sympy import divisor_count
%o A175493 from itertools import count, islice
%o A175493 def agen():
%o A175493     an = 1
%o A175493     for k in count(2):
%o A175493         yield an
%o A175493         an *= k**divisor_count(k)
%o A175493 print(list(islice(agen(), 14))) # _Michael S. Branicky_, May 03 2022
%o A175493 (PARI) a(n) = prod(k=1, n, k^numdiv(k)); \\ _Michel Marcus_, May 03 2022
%Y A175493 Cf. A062758.
%Y A175493 Cf. A174939 (sum instead of product).
%K A175493 nonn
%O A175493 1,2
%A A175493 _Leroy Quet_, May 30 2010
%E A175493 a(6) onwards from _Robert G. Wilson v_ and _Jon E. Schoenfield_, Jun 11 2010
%E A175493 a(14) and beyond from _Michael S. Branicky_, May 03 2022