A297492 a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^6*H(4*p-k^2) where H() is the Hurwitz class number and p is the n-th prime.

33, 308, 2874, 11528, 72060, 141218, 414918, 648260, 1394328, 3528690, 4608800, 9358298, 14113470, 17077148, 24378288, 39426858, 60555180, 69195410, 100714868, 127012680, 141942878, 194693840, 237229188, 313639470, 442561238, 520209690, 562658408, 655294428

Offset: 1

Author

Seiichi Manyama, Dec 31 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• N. Lygeros, O. Rozier, A new solution to the equation tau(p) == 0 (mod p), J. Int. Seq. 13 (2010) # 10.7.4.

Crossrefs

(1/2) * Sum_{|k|<=2*sqrt(p)} k^m*H(4*p-k^2): A000040 (m=0), A084920 (m=2), A297491 (m=4), this sequence (m=6), A297493 (m=8), A297494 (m=10).

Cf. A259825.

Programs

PARI

b(n) = 5*n^4 - 9*n^2 - 5*n - 1;
a(n) = b(prime(n)); \\ Michel Marcus, Jan 01 2018

Formula

Let b(n) = 5*n^4 - 9*n^2 - 5*n - 1.

a(n) = b(prime(n)).