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

1,1

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

Links

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

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

Example

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.

Crossrefs

Cf. A000005, A001597, A175064.

Sequence in context: A288756 A019279 A061652 * A278913 A306979 A380060

Adjacent sequences: A175062 A175063 A175064 * A175066 A175067 A175068

Keyword

nonn

Author

Jaroslav Krizek, Jan 23 2010

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

Status

approved