A175065 Smallest number m for which there are exactly n ways to write m as x^y with x >= 2, y >= 1.

2, 4, 16, 64, 65536, 4096, 18446744073709551616, 16777216, 68719476736, 281474976710656

Offset: 1

Author

Jaroslav Krizek, Jan 23 2010

Keywords

• nonn

Comments

a(11) is 2^1024 and is too big to display. - Joerg Arndt, Aug 17 2016.

a(n) is the smallest order of a finite field with exactly n subfields. - Jianing Song, Feb 02 2025

Examples

			For n = 6, a(6) = 4096: there are 6 ways to write 4096 as x^y: 4096^1 = 64^2 = 16^3 = 8^4 = 4^6 = 2^12.
a(7) = 2^64, a(8) = 16777216. See A175064, A001597.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A000005, A001597, A175064.

Formula

a(n) = 2^d(s) where s is the least number having d(s) = A000005(s) = n. - David A. Corneth, Aug 17 2016

a(n) = 2^A005179(n). - Joerg Arndt, Aug 17 2016

Extensions

More terms from David A. Corneth and Joerg Arndt, Aug 17 2016

Edited by N. J. A. Sloane, Aug 18 2016

a(1) prepended by Jianing Song, Feb 02 2025