cp's OEIS Frontend

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

%I A258211 #53 Feb 16 2025 08:33:25
%S A258211 18,50,54,90,98,126,150,162,198,234,242,250,270,294,306,338,342,350,
%T A258211 378,414,450,486,490,522,550,558,578,594,630,650,666,686,702,722,726,
%U A258211 738,750,774,810,846,850,882,918,950,954,990,1014,1026,1050,1058,1062,1078,1098,1134,1150
%N A258211 Nonsquarefree numbers of the form 4*k + 2.
%C A258211 The asymptotic density of this sequence is 1/4 - 2/Pi^2 = 0.047357... (A190357) - _Amiram Eldar_, Feb 10 2021
%C A258211 From _Peter Munn_, Jan 20 2022: (Start)
%C A258211 Even numbers whose square part is odd (and nontrivial).
%C A258211 If m is in the sequence then every odd multiple of m is in the sequence.
%C A258211 Closed under the operation A059896(.,.).
%C A258211 (End)
%H A258211 Amiram Eldar, <a href="/A258211/b258211.txt">Table of n, a(n) for n = 1..10000</a>
%H A258211 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarePart.html">Square Part</a>.
%F A258211 a(n) = 2*A053850(n). - _Charles R Greathouse IV_, May 26 2015
%e A258211 18 is in this sequence because 4 * 4 + 2 = 18 = 2 * 3^2.
%p A258211 remove(numtheory:-issqrfree, [4*i+2 $ i=0..1000]); # _Robert Israel_, May 27 2015
%t A258211 Select [Range[300], ! SquareFreeQ[(4 # - 2)] &] 4 - 2 (* _Vincenzo Librandi_, May 24 2015 *)
%o A258211 (Magma) [n*4+2: n in [1..300] | not IsSquarefree(4*n+2)];
%o A258211 (PARI) select(n->!issquarefree(n), vector(50,n,2*n+9))*2 \\ _Charles R Greathouse IV_, May 26 2015
%Y A258211 Intersection of A016825 and either A013929 or A335437.
%Y A258211 Cf. A039956, A053850, A059896, A190357.
%K A258211 nonn,easy
%O A258211 1,1
%A A258211 _Juri-Stepan Gerasimov_, May 23 2015