A127921 1/12 of product of three numbers: n-th prime, previous and following number.

2, 10, 28, 110, 182, 408, 570, 1012, 2030, 2480, 4218, 5740, 6622, 8648, 12402, 17110, 18910, 25058, 29820, 32412, 41080, 47642, 58740, 76048, 85850, 91052, 102078, 107910, 120232, 170688, 187330, 214268, 223790, 275650, 286900, 322478, 360882, 388108, 431462

Offset: 2

Author

Artur Jasinski, Feb 06 2007

Keywords

• nonn
• easy

Comments

Summation of products of partitions into two parts of prime(n): a(6) = (1*12) + (2*11) + (3*10) + (4*9) + (5*8) + (6*7) = 182. - César Aguilera, Feb 20 2018

Links

• G. C. Greubel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000040, A036689, A034953, A127917, A127918, A127919, A127920.

Programs

Magma

[(NthPrime(n) + 1)*NthPrime(n)*(NthPrime(n) - 1)/12: n in [2..50]]; // G. C. Greubel, Apr 30 2018

Maple

a:= n-> (p->p*(p^2-1)/12)(ithprime(n)):
seq(a(n), n=2..40);  # Alois P. Heinz, Mar 08 2022

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1)/12, {n, 2, 100}]
((#-1)#(#+1))/12&/@Prime[Range[2,40]] (* Harvey P. Dale, Mar 08 2022 *)

PARI

a(n,p=prime(n))=binomial(p+1,3)/2 \\ Charles R Greathouse IV, Feb 28 2018

Formula

a(n) ~ (n log n)^3/12. - Charles R Greathouse IV, Feb 28 2018