A078837 a(n) = Sum_{k=1..prime(n)-1} floor(k^3/prime(n)).

0, 2, 18, 60, 270, 462, 1080, 1530, 2772, 5670, 6960, 11970, 16380, 18942, 24840, 35802, 49590, 54870, 72930, 86940, 94572, 120120, 139482, 172260, 223440, 252450, 267852, 300510, 317790, 354312, 504000, 553410, 633420, 661710, 815850

Offset: 1

Author

Benoit Cloitre, Dec 08 2002

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Jean-Christophe Pain, A prime sum involving Bernoulli numbers, arXiv:2303.07934 [math.HO], 2023. See (22) p. 4.
• Eric Weisstein's World of Mathematics, Prime Sums.

Programs

Mathematica

Table[(Times@@(Prime[n]+{1,-1,-2}))/4,{n,40}] (* Harvey P. Dale, Dec 31 2020 *)

PARI

a(n) = my(p=prime(n)); sum(k=1, p-1, k^3\p); \\ Michel Marcus, Mar 16 2023

Formula

a(n) = (1/4)*(prime(n)-2)*(prime(n)-1)*(prime(n)+1).