A305633 -id:A305633

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A305635

1 and odd numbers that are not perfect powers.

+10
5

1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 123, 127, 129, 131, 133, 135, 137

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..62.

MATHEMATICA

radQ[n_]:=Or[n==1, GCD@@FactorInteger[n][[All, 2]]==1];

Select[Range[200], OddQ[#]&&radQ[#]&]

PROG

(PARI) isok(n) = (n==1) || ((n % 2) && !ispower(n)); \\ Michel Marcus, Jun 08 2018

(Magma) [1] cat [n : n in [3..200 by 2] | not IsPower(n) ]; // Vincenzo Librandi, Jul 06 2018

CROSSREFS

Cf. A001597, A005117, A007916, A039956, A056911.

Cf. A305630, A305631, A305632, A305633, A305634.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 07 2018

STATUS

approved

A305634

Even numbers that are not perfect powers.

+10
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.