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

1,1

Links

Table of n, a(n) for n=1..52.

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A016742, A077591, A109043, A245058.

Sequence in context: A290095 A275725 A242528 * A143116 A304856 A115987

Adjacent sequences: A137930 A137931 A137932 * A137934 A137935 A137936

Keyword

nonn

Author

William A. Tedeschi, Feb 29 2008

Status

approved