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

2,1

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

Formula

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

Prog

(PARI) a(n, p=prime(n))=binomial(p+1, 3)/2 \\ Charles R Greathouse IV, Feb 28 2018
(Magma) [(NthPrime(n) + 1)*NthPrime(n)*(NthPrime(n) - 1)/12: n in [2..50]]; // G. C. Greubel, Apr 30 2018

Crossrefs

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

Sequence in context: A104657 A000900 A124023 * A371943 A106184 A327696

Adjacent sequences: A127918 A127919 A127920 * A127922 A127923 A127924

Keyword

nonn,easy

Author

Artur Jasinski, Feb 06 2007

Status

approved