A084921 - OEIS

%I #61 Oct 26 2025 08:17:14

%S 3,4,12,24,60,84,144,180,264,420,480,684,840,924,1104,1404,1740,1860,

%T 2244,2520,2664,3120,3444,3960,4704,5100,5304,5724,5940,6384,8064,

%U 8580,9384,9660,11100,11400,12324,13284,13944,14964,16020,16380

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

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

%H Reinhard Zumkeller, <a href="/A084921/b084921.txt">Table of n, a(n) for n = 1..10000</a>

%H Christian Krause, <a href="https://github.com/ckrause/loda/blob/master/programs/oeis/084/A084921.asm">LODA program for A084921</a> (see also <a href="https://github.com/loda-lang/loda-programs/blob/main/oeis/084/A084921.asm">new repository</a>)

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

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

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

%F a(n) = A009286(A000040(n)). - _Enrique Pérez Herrero_, May 17 2012

%F a(n) ~ 0.5 n^2 log^2 n. - _Charles R Greathouse IV_, May 15 2013

%F Product_{n>=1} (1 + 1/a(n)) = 2. - _Amiram Eldar_, Jan 23 2021

%F a(n) = (A000040(n)^2 - 1) / 2 for n > 1. - _Christian Krause_, Mar 27 2021

%F a(n) = (3/2)*A024700(n-2), for n > 1. - _G. C. Greubel_, May 03 2024

%t LCM[#-1,#+1]&/@Prime[Range[50]] (* _Harvey P. Dale_, Oct 09 2018 *)

%o (PARI) a(n)=if(n<2,3,(prime(n)^2-1)/2) \\ _Charles R Greathouse IV_, May 15 2013

%o (Haskell)

%o a084921 n = lcm (p - 1) (p + 1)  where p = a000040 n

%o -- _Reinhard Zumkeller_, Jun 01 2013

%o (Magma) [3] cat [(p^2-1)/2: p in PrimesInInterval(3,300)]; // _G. C. Greubel_, May 03 2024

%o (SageMath) [3]+[(n^2-1)/2 for n in prime_range(3,301)] # _G. C. Greubel_, May 03 2024

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 11 2003