A032444 a(1) = 1, a(2) = 16, a(n) = lcm(48, 2n^2) for n>2.

1, 16, 144, 96, 1200, 144, 2352, 384, 1296, 1200, 5808, 288, 8112, 2352, 3600, 1536, 13872, 1296, 17328, 2400, 7056, 5808, 25392, 1152, 30000, 8112, 11664, 4704, 40368, 3600, 46128, 6144, 17424, 13872, 58800, 2592, 65712, 17328, 24336, 9600

Offset

1,2

Comments

In the M. Reid reference the following is proved: Let S(n) be the set of all groups whose order is a product of primes congruent to 1 mod n. Then, a(n) = gcd{|G| - |cc(G)| : G in S(n)}, where |cc(G)| is the number of conjugacy classes of G. - Eric M. Schmidt, Apr 18 2013

Links

Table of n, a(n) for n=1..40.

Michael Reid, The number of conjugacy classes, Amer. Math. Monthly, 105 (1998), 359-361.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,1).

Index to divisibility sequences.

Formula

a(n) = 3a(n-12) - 3a(n-24) + a(n-36) for n > 38. - Charles R Greathouse IV, Apr 18 2013

Sum_{n>=1} 1/a(n) = 11*Pi^2/1296 + 49/48. - Amiram Eldar, Oct 08 2023

Mathematica

a[n_] := LCM[48, 2*n^2]; a[1] = 1; a[2] = 16; Array[a, 40] (* Amiram Eldar, Oct 08 2023 *)

Prog

(Magma) [1, 16] cat [ LCM(48, 2*n^2) : n in [3..10] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
(PARI) a(n)=if(n>2, lcm(48, 2*n^2), 15*n-14) \\ Charles R Greathouse IV, Apr 18 2013

Crossrefs

Sequence in context: A213349 A336239 A332105 * A358263 A358262 A328224

Adjacent sequences: A032441 A032442 A032443 * A032445 A032446 A032447

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Definition rewritten by Eric M. Schmidt, Apr 18 2013

Status

approved