A258211 Nonsquarefree numbers of the form 4*k + 2.

18, 50, 54, 90, 98, 126, 150, 162, 198, 234, 242, 250, 270, 294, 306, 338, 342, 350, 378, 414, 450, 486, 490, 522, 550, 558, 578, 594, 630, 650, 666, 686, 702, 722, 726, 738, 750, 774, 810, 846, 850, 882, 918, 950, 954, 990, 1014, 1026, 1050, 1058, 1062, 1078, 1098, 1134, 1150

Offset: 1

Author

Juri-Stepan Gerasimov, May 23 2015

Keywords

• nonn
• easy

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)

Examples

			18 is in this sequence because 4 * 4 + 2 = 18 = 2 * 3^2.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Square Part.

Crossrefs

Intersection of A016825 and either A013929 or A335437.

Cf. A039956, A053850, A059896, A190357.

Programs

Magma

[n*4+2: n in [1..300] | not IsSquarefree(4*n+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 *)

PARI

select(n->!issquarefree(n), vector(50,n,2*n+9))*2 \\ Charles R Greathouse IV, May 26 2015

Formula

a(n) = 2*A053850(n). - Charles R Greathouse IV, May 26 2015