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A146209 Integers a(n) for which the factorization in the real quadratic field Q(sqrt(a(n)) is not unique. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 21 18:43 EDT 2019. Contains 328308 sequences. (Running on oeis4.)