A361559 a(n) = Sum_{k=1..prime(n)-1} floor(k^5/prime(n)).

0, 10, 258, 1740, 20070, 48510, 196920, 350370, 937860, 3075030, 4322160, 10641330, 17925180, 22825110, 35827560, 65816010, 113180910, 133937670, 215070570, 288148140, 331474860, 493573080, 633015810, 899599140, 1387338960, 1700082450, 1876303260, 2272556790, 2494333710

Offset: 1

Author

Michel Marcus, Mar 15 2023

Keywords

• nonn

Links

• Jean-Christophe Pain, A prime sum involving Bernoulli numbers, arXiv:2303.07934 [math.HO], 2023. See (23) p. 4.

Crossrefs

Cf. A078837 (for k^3).

Programs

Maple

a:= n-> (p-> (p-2)*(p-1)*(p+1)*(2*p^2-2*p+3)/12)(ithprime(n)):
seq(a(n), n=1..29);  # Alois P. Heinz, Mar 15 2023

PARI

a(n) = my(p=prime(n)); sum(k=1, p-1, k^5\p);

Formula

a(n) = (p-2)*(p-1)*(p+1)*(2*p^2-2*p+3)/12 where p=prime(n).