A293205 - OEIS

%I #12 Oct 04 2017 02:05:55

%S 1,2,3,4,5,7,8,9,11,13,15,16,17,18,19,21,23,25,27,29,31,32,33,35,37,

%T 39,41,43,45,47,49,50,51,53,55,57,59,61,63,64,65,67,69,71,73,75,77,79,

%U 81,83,85,87,89,91,93,95,97,98,99,101,103,105,107,108,109

%N Numbers n > 0 such that 2*n = (4*k-2)^m where k, m > 0.

%C One half times all singly even numbers (A016825) and all powers of them.

%H Robert Israel, <a href="/A293205/b293205.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 = 2^1/2, 2 = 2^2/2, 3 = 6^1/2, 4 = 2^3/2, 5 = 10^1/2, 7 = 14^1/2, ...

%p filter:= proc(n) local v,m;

%p   if n::odd then true

%p   else v:= padic:-ordp(n,2); m:= n/2^v; type(simplify(m^(1/(v+1))),integer) fi

%p end proc:

%p select(filter, [$1..200]); # _Robert Israel_, Oct 03 2017

%t Block[{nn = 120, s}, s = Range[2, 2 nn, 4]; Union@ Flatten@ Map[#^Range@ Floor@ Log[#, 2 nn]/2 &, s]] (* _Michael De Vlieger_, Oct 02 2017 *)

%o (PARI) {a(n) = my(cnt, m, k); if( n<1, return(0), while( cnt<n, m++; k=2*m; ispower(k, ,&k); if(k%4==2, cnt++)); m)};

%Y Cf. A016825.

%K nonn

%O 1,2

%A _Michael Somos_, Oct 02 2017