A127919 1/3 of product of three numbers: the n-th prime, the previous number and the following number.

2, 8, 40, 112, 440, 728, 1632, 2280, 4048, 8120, 9920, 16872, 22960, 26488, 34592, 49608, 68440, 75640, 100232, 119280, 129648, 164320, 190568, 234960, 304192, 343400, 364208, 408312, 431640, 480928, 682752, 749320, 857072, 895160, 1102600

Offset: 1

Author

Artur Jasinski, Feb 06 2007

Keywords

• nonn
• easy

Comments

Number of irreducible monic cubic polynomials over GF(prime(n)). - Robert Israel, Jan 06 2015

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036689, A034953, A127917, A127918, A127920.

Programs

Magma

[(p^3 - p) div 3: p in PrimesUpTo(150)]; // Vincenzo Librandi, Jan 08 2015

Maple

seq((ithprime(n)^3 - ithprime(n))/3, n=1..100); # Robert Israel, Jan 06 2015

Mathematica

Table[(Prime[n] + 1) Prime[n] (Prime[n] - 1)/3, {n, 100}]

PARI

forprime(p=2,1e3,print1(2*binomial(p+1,3)", ")) \\ Charles R Greathouse IV, Jun 16 2011

Formula

a(n) = (prime(n)^3 - prime(n))/3. - Wesley Ivan Hurt, Oct 15 2023