A302974 a(n) = numerator of tau(n)^n / n^tau(n).

1, 1, 8, 81, 32, 256, 128, 16, 27, 65536, 2048, 729, 8192, 16777216, 1073741824, 152587890625, 131072, 2985984, 524288, 892616806656, 4398046511104, 1099511627776, 8388608, 281474976710656, 847288609443, 281474976710656, 18014398509481984, 1499253470328324096

Offset: 1

Author

Jaroslav Krizek, Apr 16 2018

Keywords

• nonn
• frac

Comments

tau(n) = the number of the divisors of n (A000005).

a(n) <= A302975(n) only for numbers n = 1, 2 and 3.

Examples

			For n = 6; tau(6)^6 / 6^tau(6) = 4^6 / 6^4 = 256 / 81; a(6) = 256.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..779

Crossrefs

Cf. A000005, A120737, A302975, A302976.

Programs

Magma

[Numerator((NumberOfDivisors(n)^n) / (n^NumberOfDivisors(n))): n in[1..100]];

Mathematica

Numerator[#[[2]]^#[[1]]/#[[1]]^#[[2]]]&/@Table[{n,DivisorSigma[0,n]},{n,30}] (* Harvey P. Dale, May 29 2023 *)