A297491 a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^4*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime.

9, 44, 234, 664, 2628, 4354, 9774, 13660, 24264, 48690, 59488, 101194, 137718, 158884, 207504, 297594, 410580, 453778, 601324, 715608, 777814, 985840, 1143324, 1409670, 1825054, 2060298, 2185144, 2449764, 2589730, 2885454, 4096384, 4495788, 5142294

Offset

1,1

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.

Formula

Let b(n) = 2*n^3 - 3*n - 1.

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

Crossrefs

(1/2) * Sum_{|k|<=2*sqrt(p)} k^m*H(4*p-k^2): A000040 (m=0), A084920 (m=2), this sequence (m=4), A297492 (m=6), A297493 (m=8), A297494 (m=10).

Cf. A259825.

Sequence in context: A144109 A099867 A228603 * A104470 A282722 A084023

Adjacent sequences: A297488 A297489 A297490 * A297492 A297493 A297494

Keyword

nonn

Author

Seiichi Manyama, Dec 31 2017

Status

approved