A061574 Simple quadratic fields (i.e., with a unique prime factorization).

-163, -67, -43, -19, -11, -7, -3, -2, -1, 1, 2, 3, 5, 6, 7, 11, 13, 14, 17, 19, 21, 22, 23, 29, 31, 33, 37, 38, 41, 43, 46, 47, 53, 57, 59, 61, 62, 67, 69, 71, 73, 77, 83, 86, 89, 93, 94, 97, 101, 103, 107, 109, 113, 118, 127, 129, 131, 133, 134, 137, 139, 141, 149

Offset

-9,1

Comments

-9 <= m < 0: a(m)= -A003173(-m); a(0) = 1; n > 0: a(n) = A003172(n).

Squarefree values of n for which the quadratic field Q[ sqrt(n) ] is a unique factorization domain, but not necessarily Euclidean. All negative values are listed. - Alonso del Arte, Feb 10 2011

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, ch. 14.

Links

Daniel Forgues (copying T. D. Noe's b003172.txt), Table of n, a(n) for n = -9..1000

Index entries for sequences related to quadratic fields

Mathematica

Select[Range[-200, 200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] == 1 &] (* T. D. Noe, Feb 10 2011 *)

Crossrefs

Union of A003173 and A003172. Some subsequences: A048981 (requires the fields to be Euclidean), A003174, A003172, see also A003173.

Sequence in context: A214236 A349511 A030442 * A185444 A217546 A057604

Adjacent sequences: A061571 A061572 A061573 * A061575 A061576 A061577

Keyword

sign

Author

Frank Ellermann, May 17 2001

Status

approved