A305634 Even numbers that are not perfect powers.

2, 6, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 34, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 130, 132, 134, 136, 138

Offset: 1

Author

Gus Wiseman, Jun 07 2018

Keywords

• nonn

Comments

Perfect powers are of the form m^k where m > 0 and k > 1 (A001597).

Examples

			10 is in the sequence since it is even and is not a power of an integer.  17 is not in the sequence since it is odd, and 36 is not in the sequence since it is a power of an integer (36 = 6^2).
		

Links

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

Crossrefs

Cf. A001597, A005117, A007916, A039956.

Cf. A305630, A305631, A305632, A305633, A305635.

Cf. A005843, A001597.

Programs

Maple

N:= 1000:
S:={seq(i,i=2..N,2)} minus {seq(seq(e^m,m=2..floor(log[e](N))),e=2..floor(sqrt(N)),2)}:
sort(convert(S,list)); # Robert Israel, Jan 24 2019

Mathematica

radQ[n_]:=Or[n==1,GCD@@FactorInteger[n][[All,2]]==1];
Select[Range[200],EvenQ[#]&&radQ[#]&]

PARI

isok(n) = !(n % 2) && !ispower(n); \\ Michel Marcus, Jun 08 2018

Formula

A005843 \ A001597. - Eric Chen, Jun 14 2018