A210490 Union of positive squares (A000290 \ {0}) and squarefree numbers (A005117).

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

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: A239289 A131511 A361634 * 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