%I #17 Jul 06 2022 06:58:06

%S 2,4,18,16,50,36,98,64,162,100,242,144,338,196,450,256,578,324,722,

%T 400,882,484,1058,576,1250,676,1458,784,1682,900,1922,1024,2178,1156,

%U 2450,1296,2738,1444,3042,1600,3362,1764,3698,1936,4050,2116,4418,2304,4802,2500,5202,2704

%N Least common multiple of n^2 and 2.

%F a(n) = lcm(n^2, 2).

%F From _R. J. Mathar_, Mar 06 2008: (Start)

%F O.g.f.: -2x(1 + 6x^2 + x^4 + 2x^3 + 2x)/((-1+x)^3 * (x+1)^3).

%F a(2n) = A016742(n).

%F a(2n+1) = A077591(n). (End)

%F a(n) = n*A109043(n). - _Michel Marcus_, Mar 13 2018

%F From _Amiram Eldar_, Jul 06 2022: (Start)

%F Sum_{n>=1} 1/a(n) = 5*Pi^2/48.

%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/48 = -A245058. (End)

%t LCM[Range[60]^2,2] (* _Harvey P. Dale_, Jun 06 2018 *)

%o (PARI) a(n) = lcm(n^2, 2); \\ _Michel Marcus_, Mar 13 2018

%Y Cf. A016742, A077591, A109043, A245058.

%K nonn

%O 1,1

%A _William A. Tedeschi_, Feb 29 2008