A146209 Integers a(n) for which the factorization in the real quadratic field Q(sqrt(a(n))) is not unique.

10, 15, 26, 30, 34, 35, 39, 42, 51, 55, 58, 65, 66, 70, 74, 78, 79, 82, 85, 87, 91, 95, 102, 105, 106, 110, 111, 114, 115, 119, 122, 123, 130, 138, 142, 143, 145, 146, 154, 155, 159, 165, 170, 174, 178, 182, 183, 185, 186, 187, 190, 194, 195

Offset

1,1

Comments

The class number of Q(sqrt(a(n))) is greater than 1.

Contains A029702, A053330 and A051990 as subsequences. See A219361 for positive integers D for which Q(sqrt D) is a UFD. - M. F. Hasler, Oct 30 2014

References

Z. I. Borevich and I. R. Shafarevich, Zahlentheorie. Birkhäuser Verlag, Basel und Stuttgart (1966).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

For n = 6, a(6) = 35 since 35 is the sixth positive squarefree integer u for which the factorization in Q(sqrt(u)) is not unique.

Mathematica

Select[Range[200], SquareFreeQ[#] && NumberFieldClassNumber[Sqrt[#]] > 1 &] (* Alonso del Arte, Sep 05 2012 *)

Crossrefs

Cf. A003172.

Sequence in context: A001750 A231643 A276541 * A029702 A053330 A051990

Adjacent sequences: A146206 A146207 A146208 * A146210 A146211 A146212

Keyword

nonn

Author

Pahikkala Jussi, Oct 28 2008

Status

approved