A165315 a(1)=2. If s is the largest integer such that n = r^s, r = positive integer, then a(n) = the smallest integer > a(n-1) such that a(n) = t^s, t = positive integer.

2, 3, 4, 9, 10, 11, 12, 27, 36, 37, 38, 39, 40, 41, 42, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 125, 126, 127, 128, 129, 243, 244, 245, 246, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298

Offset

1,1

Comments

The variable s need not necessarily be the largest integer such that a(n) = t^s, t = some positive integer. (For example, a(3) = 4 because 4 is a first power, like 3.)

If a(1) had equaled 1 instead, then the sequence would have been just the sequence of positive integers, obviously.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

a(9) = 36 because 9 = 3^2, and because 36 is the smallest square > a(8) = 27.

Mathematica

FoldList[Ceiling[(#1 + 1)^(1/(s = GCD @@ FactorInteger[#2][[All, 2]]))]^s &, 2, Range[2, 58]] (* Ivan Neretin, Apr 26 2017 *)

Crossrefs

Sequence in context: A047454 A373788 A081870 * A284681 A309346 A047339

Adjacent sequences: A165312 A165313 A165314 * A165316 A165317 A165318

Keyword

nonn

Author

Leroy Quet, Sep 14 2009

Extensions

Edited by Ray Chandler, Mar 14 2010

Status

approved