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A001983 Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.

%I A001983 #52 Jan 02 2023 09:02:24
%S A001983 1,4,5,9,10,13,16,17,20,25,26,29,34,36,37,40,41,45,49,50,52,53,58,61,
%T A001983 64,65,68,73,74,80,81,82,85,89,90,97,100,101,104,106,109,113,116,117,
%U A001983 121,122,125,130,136,137,144,145,146,148,149,153,157,160,164
%N A001983 Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.
%C A001983 This sequence lists the values of A000404(n)/2 when A000404(n) is an even number. In other words, sequence lists integers n that are the average of two nonzero squares. - _Altug Alkan_, May 26 2016
%H A001983 T. D. Noe, <a href="/A001983/b001983.txt">Table of n, a(n) for n = 1..1000</a>
%H A001983 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~twosquares.en.html">Two squares</a>
%H A001983 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A001983 A025435(a(n)) > 0. - _Reinhard Zumkeller_, Dec 20 2013
%t A001983 upto=200;max=Floor[Sqrt[upto]];s=Total/@((Subsets[Range[0,max], {2}])^2);Union[Select[s,#<=upto&]]  (* _Harvey P. Dale_, Apr 01 2011 *)
%t A001983 selQ[n_] := Select[ PowersRepresentations[n, 2, 2], 0 <= #[[1]] < #[[2]] &] != {}; Select[Range[200], selQ] (* _Jean-François Alcover_, Oct 03 2013 *)
%o A001983 (Haskell)
%o A001983 a001983 n = a001983_list !! (n-1)
%o A001983 a001983_list = [x | x <- [0..], a025435 x > 0]
%o A001983 -- _Reinhard Zumkeller_, Dec 20 2013
%o A001983 (PARI) list(lim)=my(v=List()); for(x=0,sqrtint(lim\4), for(y=x+1, sqrtint(lim\1-x^2), listput(v, x^2+y^2))); Set(v) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y A001983 Cf. A000404, subsequence of A001481, A004435 (complement), A025435, A004431.
%Y A001983 Union of A000290 and A004431 excluding 0.
%K A001983 nonn,easy,nice
%O A001983 1,2
%A A001983 _N. J. A. Sloane_