A165315 - OEIS

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.

%I #10 Apr 26 2017 22:26:53

%S 2,3,4,9,10,11,12,27,36,37,38,39,40,41,42,81,82,83,84,85,86,87,88,89,

%T 100,101,125,126,127,128,129,243,244,245,246,256,257,258,259,260,261,

%U 262,263,264,265,266,267,268,289,290,291,292,293,294,295,296,297,298

%N 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.

%C 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.)

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

%H Ivan Neretin, <a href="/A165315/b165315.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%K nonn

%O 1,1

%A _Leroy Quet_, Sep 14 2009

%E Edited by _Ray Chandler_, Mar 14 2010