A084921 a(n) = lcm(p-1, p+1) where p is the n-th prime.

3, 4, 12, 24, 60, 84, 144, 180, 264, 420, 480, 684, 840, 924, 1104, 1404, 1740, 1860, 2244, 2520, 2664, 3120, 3444, 3960, 4704, 5100, 5304, 5724, 5940, 6384, 8064, 8580, 9384, 9660, 11100, 11400, 12324, 13284, 13944, 14964, 16020, 16380

Offset: 1

Author

Reinhard Zumkeller, Jun 11 2003

Keywords

• nonn

Comments

This sequence consists of terms of sequences A055523 and A055527 for prime n > 2. - Toni Lassila (tlassila(AT)cc.hut.fi), Feb 02 2004

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Christian Krause, LODA program for A084921
• Index entries for sequences related to lcm's

Crossrefs

Cf. A000040, A006093, A008864, A009286, A024700, A055523, A055527, A084920, A084922.

Programs

Haskell

a084921 n = lcm (p - 1) (p + 1)  where p = a000040 n
-- Reinhard Zumkeller, Jun 01 2013

Magma

[3] cat [(p^2-1)/2: p in PrimesInInterval(3,300)]; // G. C. Greubel, May 03 2024

Mathematica

LCM[#-1,#+1]&/@Prime[Range[50]] (* Harvey P. Dale, Oct 09 2018 *)

PARI

a(n)=if(n<2,3,(prime(n)^2-1)/2) \\ Charles R Greathouse IV, May 15 2013

SageMath

[3]+[(n^2-1)/2 for n in prime_range(3,301)] # G. C. Greubel, May 03 2024

Formula

a(n) = A084920(n)/2 for n > 1.

a(n) = 3*A084922(n) for n > 2.

a(n) = A009286(A000040(n)). - Enrique Pérez Herrero, May 17 2012

a(n) ~ 0.5 n^2 log^2 n. - Charles R Greathouse IV, May 15 2013

Product_{n>=1} (1 + 1/a(n)) = 2. - Amiram Eldar, Jan 23 2021

a(n) = (A000040(n)^2 - 1) / 2 for n > 1. - Christian Krause, Mar 27 2021

a(n) = (3/2)*A024700(n-2), for n > 1. - G. C. Greubel, May 03 2024