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A210490 Union of positive squares (A000290 \ {0}) and squarefree numbers (A005117). 3
1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 46, 47, 49, 51, 53, 55, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 91, 93, 94 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that either all exponents in the prime factorization of n (cf. A124010) are even or all are = 1.

Every positive integer can be expressed as the product of two elements of this sequence. Every integer > 1 can be expressed as the product of two distinct members of the sequence. - Franklin T. Adams-Watters, Apr 08 2016

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Square Number

Eric Weisstein's World of Mathematics, Squarefree

Wikipedia, Squarefree integer

Wikipedia, Square number

FORMULA

A008966(a(n)) + A010052(a(n)) > 0.

PROG

(Haskell)

a210490 n = a210490_list !! (n-1)

a210490_list = filter chi [1..] where

chi x = all (== 1) es || all even es where es = a124010_row x

(PARI) isok(m) = issquare(m) || issquarefree(m); \\ Michel Marcus, Feb 03 2022

CROSSREFS

Cf. A051144 (complement).

Cf. A000290, A005117.

Cf. A008966, A010052.

Sequence in context: A039217 A239289 A131511 * A340682 A166155 A342525

Adjacent sequences: A210487 A210488 A210489 * A210491 A210492 A210493

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 24 2013

EXTENSIONS

A more precise name from Michel Marcus, Feb 03 2022

STATUS

approved

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Last modified November 27 03:51 EST 2022. Contains 358362 sequences. (Running on oeis4.)