A202084 Class number of sqrt(-n).

1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 4, 2, 1, 4, 1, 1, 2, 4, 2, 3, 2, 1, 6, 1, 1, 6, 4, 3, 1, 4, 4, 2, 1, 2, 6, 4, 2, 8, 4, 1, 1, 2, 4, 5, 1, 1, 1, 2, 2, 6, 2, 4, 4, 4, 2, 3, 2, 6, 8, 1, 1, 8, 8, 1, 4, 8, 4, 7, 1, 4, 10, 1, 1, 8, 4, 5, 2, 1, 4, 3, 4, 4, 10

Offset

1,5

Comments

For class number of sqrt(n) see A202053.

If p is a prime congruent to 3 modulo 4, then a(p) divides A000927(p). - Arkadiusz Wesolowski, Apr 14 2026

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Class Number.

Wikipedia, Class number formula.

Mathematica

Table[NumberFieldClassNumber[Sqrt[-n]], {n, 100}]

Prog

(PARI) a(n)=bnfinit(x^2+n).no \\ Arkadiusz Wesolowski, Apr 14 2026
(SageMath)
def A202084(n):
    s = squarefree_part(n)
    t = s if s % 4 < 2 else 4 * s
    return QuadraticField(t, 'a').class_number()
print([A202084(-n) for n in range(1, 87)])  # Mo Li, Sep 10 2023

Crossrefs

Cf. A000927, A202053.

Sequence in context: A274888 A239702 A378399 * A337763 A109072 A100727

Adjacent sequences: A202081 A202082 A202083 * A202085 A202086 A202087

Keyword

nonn,changed

Author

Artur Jasinski, Dec 11 2011

Status

approved