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Numbers m such that the discriminant of the quadratic field Q(sqrt(m)) < m.
3

%I #16 Jun 24 2022 04:34:26

%S 4,9,16,18,20,25,27,32,36,45,48,49,50,52,54,63,64,68,72,75,80,81,84,

%T 90,96,98,99,100,108,112,116,117,121,125,126,128,132,135,144,147,148,

%U 150,153,160,162,164,169,171,175,176,180,189,192,196,198,200,207,208,212

%N Numbers m such that the discriminant of the quadratic field Q(sqrt(m)) < m.

%C Among terms are all the squares for which discriminant = 1.

%H Amiram Eldar, <a href="/A072903/b072903.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) appears to be asymptotic to C*n with C = 3.4... .

%t Select[Range[220], NumberFieldDiscriminant[Sqrt[#]] < # &] (* _Amiram Eldar_, Jun 24 2022 *)

%o (PARI) isok(m) = quaddisc(m) < m; \\ _Michel Marcus_, Feb 18 2021

%Y Cf. A037449, A072904.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Aug 10 2002