A297493 a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^8*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime.

129, 2444, 39714, 224664, 2214948, 5133114, 19734534, 34465980, 89757384, 286456170, 399954528, 969369474, 1620023118, 2055854724, 3207878544, 5850511794, 10003119540, 11817917898, 18893239884, 25249088088, 29012002734, 43064859120, 55130420604

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), A297492 (m=6), this sequence (m=8), A297494 (m=10).

Cf. A259825.

Programs

PARI

lista(nn) = forprime(p=2, nn, print1(14*p^5-28*p^3-20*p^2-7*p-1, ", ")); \\ Altug Alkan, Jan 01 2018

Formula

Let b(n) = 14*n^5 - 28*n^3 - 20*n^2 - 7*n - 1.

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