A137933 Least common multiple of n^2 and 2.

2, 4, 18, 16, 50, 36, 98, 64, 162, 100, 242, 144, 338, 196, 450, 256, 578, 324, 722, 400, 882, 484, 1058, 576, 1250, 676, 1458, 784, 1682, 900, 1922, 1024, 2178, 1156, 2450, 1296, 2738, 1444, 3042, 1600, 3362, 1764, 3698, 1936, 4050, 2116, 4418, 2304, 4802, 2500, 5202, 2704

Offset: 1

Author

William A. Tedeschi, Feb 29 2008

Keywords

• nonn

Crossrefs

Cf. A016742, A077591, A109043, A245058.

Programs

Mathematica

LCM[Range[60]^2,2] (* Harvey P. Dale, Jun 06 2018 *)

PARI

a(n) = lcm(n^2, 2); \\ Michel Marcus, Mar 13 2018

Formula

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

From R. J. Mathar, Mar 06 2008: (Start)

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

a(2n) = A016742(n).

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

a(n) = n*A109043(n). - Michel Marcus, Mar 13 2018

From Amiram Eldar, Jul 06 2022: (Start)

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

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