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A302975
a(n) = denominator of tau(n)^n / n^tau(n).
3
1, 1, 9, 64, 25, 81, 49, 1, 1, 625, 121, 1, 169, 2401, 50625, 1048576, 289, 1, 361, 15625, 194481, 14641, 529, 6561, 15625, 28561, 531441, 117649, 841, 2562890625, 961, 1, 1185921, 83521, 1500625, 262144, 1369, 130321, 2313441, 390625, 1681, 37822859361, 1849
OFFSET
1,3
COMMENTS
tau(n) = the number of the divisors of n (A000005).
Conjecture: all terms are squares.
a(n) >= A302974(n) only for numbers n = 1, 2 and 3.
LINKS
FORMULA
a(p) = p^2 for p = prime.
a(A120737(n)) = 1.
EXAMPLE
For n = 6; tau(6)^6 / 6^tau(6) = 4^6 / 6^4 = 256 / 81; a(6) = 81.
MATHEMATICA
Denominator[#[[2]]^#[[1]]/#[[1]]^#[[2]]]&/@Table[{n, DivisorSigma[0, n]}, {n, 50}] (* Harvey P. Dale, Sep 15 2019 *)
PROG
(Magma) [Denominator((NumberOfDivisors(n)^n) / (n^NumberOfDivisors(n))): n in[1..100]]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jaroslav Krizek, Apr 16 2018
STATUS
approved