A244891 Class number of maximal order O_1 in a totally definite quaternion Q(sqrt(p))-algebra D_{oo_1, oo_2}, where p = n-th prime.

1, 2, 1, 3, 4, 1, 1, 6, 7, 2, 9, 2, 2, 12, 13, 3, 16, 3, 18, 19, 3, 69, 22, 4, 4, 5, 31, 28, 5, 5, 39, 38, 6, 44, 7, 49, 7, 50, 47, 8, 54, 8, 61, 10, 9, 71, 74, 231, 66, 30, 12, 79, 14, 84, 39, 85, 12, 105, 14, 16, 104, 13, 114, 111, 19, 14, 136, 22, 116, 17, 19, 405, 151, 20, 164, 133

Offset

1,2

Links

Table of n, a(n) for n=1..76.

J. Xue, T.-C. Yang, C.-F. Yu, Supersingular abelian surfaces and Eichler class number formula, arXiv preprint arXiv:1404.2978, 2014. See Table 1.

Prog

(Sage)
def a(n):
    if n < 4: return [1, 2, 1][n-1]
    p = Primes()[n-1]
    F = NumberField(x^2 - p, names='a')
    hKi = [F.extension(x^2+i+1, names='b').class_number() for i in range(3)]
    ans = F.class_number()*F.zeta_function(100)(-1)/2 + hKi[2]/3
    if p%4 == 1: ans += hKi[0]/4
    else: ans += (3 + 5*(2 - legendre_symbol(2, p)))*hKi[0]/8 + hKi[1]/4
    return round(ans.real_part())  # Robin Visser, Feb 23 2024

Crossrefs

Sequence in context: A160188 A332864 A337569 * A322081 A279396 A161224

Adjacent sequences: A244888 A244889 A244890 * A244892 A244893 A244894

Keyword

nonn

Author

N. J. A. Sloane, Jul 13 2014

Extensions

More terms from Robin Visser, Feb 23 2024

Status

approved