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A305634 Even numbers that are not perfect powers. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A298748 A139799 A214586 * A139710 A194712 A057921

Adjacent sequences:  A305631 A305632 A305633 * A305635 A305636 A305637

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 07 2018

STATUS

approved

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Last modified August 4 12:45 EDT 2020. Contains 336201 sequences. (Running on oeis4.)