

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
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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. AdamsWatters, 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 !! (n1)
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



