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%I #28 Dec 19 2020 07:57:07
%S 4,8,9,12,16,18,20,24,27,28,32,36,40,44,45,48,49,52,54,56,60,63,64,68,
%T 72,76,80,81,84,88,90,92,96,98,99,100,104,108,112,116,117,120,121,124,
%U 126,128,132,135,136,140,144,147,148,152,153,156,160,162,164,168,171
%N x^2 + y^2 does not take on all possible values mod n.
%C Sequence gives values of n such there is not always a solution 1 < z < n to x^2 + y^2 = z (mod n). - _Benoit Cloitre_, Jan 04 2002; corrected by _Carmine Suriano_, Jun 19 2013
%C The asymptotic density of this sequence is 1- 3/(8*K^2) = 1 - (3/4) * A243379 = 0.35791..., where K is the Landau-Ramanujan constant (A064533). - _Amiram Eldar_, Dec 19 2020
%H Charles R Greathouse IV, <a href="/A053443/b053443.txt">Table of n, a(n) for n = 1..10000</a>
%F n divisible by p^2 where p = 2 or prime p == 3 (mod 4).
%t Select[Range[200], AnyTrue[FactorInteger[#], Mod[First[#1], 4] > 1 && Last[#1] > 1 &] &] (* _Amiram Eldar_, Dec 19 2020 *)
%o (PARI) is(n)=my(v=vectorsmall(n,i,1));for(x=0,n\2, for(y=0,x, v[(x^2+y^2)%n+1]=0)); vecmax(v) \\ _Charles R Greathouse IV_, Jun 19 2013
%o (PARI) is(n)=forprime(p=2,97,my(o=valuation(n,p));if(o,if(o>1&&p%4>1,return(1));n/=p^o));my(f=factor(n));for(i=1,#f[,1],if(f[i,2]>1&&f[i,1]%4>1,return(1)));0 \\ _Charles R Greathouse IV_, Jun 19 2013
%Y Complement of A240370.
%Y Cf. A053444, A064533, A243379.
%K nonn
%O 1,1
%A _David W. Wilson_
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