A302975 a(n) = denominator of tau(n)^n / n^tau(n).

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A000005, A120737, A302974, A302976.

Sequence in context: A165749 A251211 A342197 * A165447 A050792 A171671

Adjacent sequences: A302972 A302973 A302974 * A302976 A302977 A302978

Keyword

nonn,frac

Author

_Jaroslav Krizek_, Apr 16 2018

Status

approved