%I #9 Sep 08 2022 08:46:21
%S 1,1,9,64,25,81,49,1,1,625,121,1,169,2401,50625,1048576,289,1,361,
%T 15625,194481,14641,529,6561,15625,28561,531441,117649,841,2562890625,
%U 961,1,1185921,83521,1500625,262144,1369,130321,2313441,390625,1681,37822859361,1849
%N a(n) = denominator of tau(n)^n / n^tau(n).
%C tau(n) = the number of the divisors of n (A000005).
%C Conjecture: all terms are squares.
%C a(n) >= A302974(n) only for numbers n = 1, 2 and 3.
%H Harvey P. Dale, <a href="/A302975/b302975.txt">Table of n, a(n) for n = 1..1000</a>
%F a(p) = p^2 for p = prime.
%F a(A120737(n)) = 1.
%e For n = 6; tau(6)^6 / 6^tau(6) = 4^6 / 6^4 = 256 / 81; a(6) = 81.
%t Denominator[#[[2]]^#[[1]]/#[[1]]^#[[2]]]&/@Table[{n,DivisorSigma[0,n]},{n,50}] (* _Harvey P. Dale_, Sep 15 2019 *)
%o (Magma) [Denominator((NumberOfDivisors(n)^n) / (n^NumberOfDivisors(n))): n in[1..100]]
%Y Cf. A000005, A120737, A302974, A302976.
%K nonn,frac
%O 1,3
%A _Jaroslav Krizek_, Apr 16 2018
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