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

1,1

Comments

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

Links

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

Formula

A005843 \ A001597. - Eric Chen, Jun 14 2018

Example

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).

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[#]&]

Prog

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

Crossrefs

Cf. A001597, A005117, A007916, A039956.

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

Cf. A005843, A001597.

Sequence in context: A139799 A214586 A337687 * A139710 A194712 A057921

Adjacent sequences: A305631 A305632 A305633 * A305635 A305636 A305637

Keyword

nonn

Author

Gus Wiseman, Jun 07 2018

Status

approved