cp's OEIS Frontend

A137933 Least common multiple of n^2 and 2.

%I A137933 #17 Jul 06 2022 06:58:06
%S A137933 2,4,18,16,50,36,98,64,162,100,242,144,338,196,450,256,578,324,722,
%T A137933 400,882,484,1058,576,1250,676,1458,784,1682,900,1922,1024,2178,1156,
%U A137933 2450,1296,2738,1444,3042,1600,3362,1764,3698,1936,4050,2116,4418,2304,4802,2500,5202,2704
%N A137933 Least common multiple of n^2 and 2.
%F A137933 a(n) = lcm(n^2, 2).
%F A137933 From _R. J. Mathar_, Mar 06 2008: (Start)
%F A137933 O.g.f.: -2x(1 + 6x^2 + x^4 + 2x^3 + 2x)/((-1+x)^3 * (x+1)^3).
%F A137933 a(2n) = A016742(n).
%F A137933 a(2n+1) = A077591(n). (End)
%F A137933 a(n) = n*A109043(n). - _Michel Marcus_, Mar 13 2018
%F A137933 From _Amiram Eldar_, Jul 06 2022: (Start)
%F A137933 Sum_{n>=1} 1/a(n) = 5*Pi^2/48.
%F A137933 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/48 = -A245058. (End)
%t A137933 LCM[Range[60]^2,2] (* _Harvey P. Dale_, Jun 06 2018 *)
%o A137933 (PARI) a(n) = lcm(n^2, 2); \\ _Michel Marcus_, Mar 13 2018
%Y A137933 Cf. A016742, A077591, A109043, A245058.
%K A137933 nonn
%O A137933 1,1
%A A137933 _William A. Tedeschi_, Feb 29 2008