A367669 Number of degree 3 number fields unramified outside the first n prime numbers.

0, 9, 32, 108, 360, 1168, 3638, 11492, 35638, 111059

Offset: 1

Author

Robin Visser, Nov 26 2023

Keywords

• nonn
• more

Comments

B. Matschke showed that a(11) = 340618 assuming the Generalized Riemann Hypothesis.

Examples

			For n = 1, there are no cubic number fields unramified away from 2, so a(1) = 0.
For n = 2, the a(2) = 9 cubic number fields unramified away from {2,3} can be given by Q(a) where a is a root of x^3 - 3x - 1, x^3 - 2, x^3 + 3x - 2, x^3 - 3, x^3 - 3x - 4, x^3 - 3x - 10, x^3 - 12, x^3 - 6, or x^3 - 9x - 6.
		

Links

• K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), no. 219, 1213-1237.
• J. W. Jones and D. P. Roberts, A database of number fields, LMS J. Comput. Math. 17 (2014), no. 1, 595-618.
• B. Matschke, Number fields unramified outside S.

Crossrefs

Cf. A126646 (degree 2), A368057 (degree 4).