OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1/4 - 2/Pi^2 = 0.047357... (A190357) - Amiram Eldar, Feb 10 2021
From Peter Munn, Jan 20 2022: (Start)
Even numbers whose square part is odd (and nontrivial).
If m is in the sequence then every odd multiple of m is in the sequence.
Closed under the operation A059896(.,.).
(End)
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Square Part.
FORMULA
a(n) = 2*A053850(n). - Charles R Greathouse IV, May 26 2015
EXAMPLE
18 is in this sequence because 4 * 4 + 2 = 18 = 2 * 3^2.
MAPLE
remove(numtheory:-issqrfree, [4*i+2 $ i=0..1000]); # Robert Israel, May 27 2015
MATHEMATICA
Select [Range[300], ! SquareFreeQ[(4 # - 2)] &] 4 - 2 (* Vincenzo Librandi, May 24 2015 *)
PROG
(Magma) [n*4+2: n in [1..300] | not IsSquarefree(4*n+2)];
(PARI) select(n->!issquarefree(n), vector(50, n, 2*n+9))*2 \\ Charles R Greathouse IV, May 26 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, May 23 2015
STATUS
approved