A293205 Numbers n > 0 such that 2*n = (4*k-2)^m where k, m > 0.

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, 39, 41, 43, 45, 47, 49, 50, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 98, 99, 101, 103, 105, 107, 108, 109

Offset

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

filter:= proc(n) local v, m;
  if n::odd then true
  else v:= padic:-ordp(n, 2); m:= n/2^v; type(simplify(m^(1/(v+1))), integer) fi
end proc:
select(filter, [$1..200]); # Robert Israel, Oct 03 2017

Mathematica

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 *)

Prog

(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)};

Crossrefs

Cf. A016825.

Sequence in context: A210576 A191848 A360613 * A046687 A175418 A078175

Adjacent sequences: A293202 A293203 A293204 * A293206 A293207 A293208

Keyword

nonn

Author

Michael Somos, Oct 02 2017

Status

approved