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A192336 Sums of two or more distinct squares.

%I A192336 #18 May 10 2021 11:30:00
%S A192336 5,10,13,14,17,20,21,25,26,29,30,34,35,37,38,39,40,41,42,45,46,49,50,
%T A192336 51,52,53,54,55,56,57,58,59,61,62,63,65,66,68,69,70,71,73,74,75,77,78,
%U A192336 79,80,81,82,83,84,85,86,87,88,89,90,91,93,94,95,97,98,99,100,101,102,103,104
%N A192336 Sums of two or more distinct squares.
%H A192336 Charles R Greathouse IV, <a href="/A192336/b192336.txt">Table of n, a(n) for n = 1..10000</a>
%H A192336 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%H A192336 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A192336 a(n) = n + 37 for n >= 92.
%e A192336 5 = 1^2 + 2^2 and 25 = 3^2 + 4^2 are members, but 2 = 1^2 + 1^2 and 36 = 6^2 are not.
%o A192336 (PARI) upto(lim)={
%o A192336   my(x='x,A=prod(k=1,sqrt(lim),1+x^(k^2),1+O(x^floor(lim+1))),v=List());
%o A192336   A-=sum(k=0,sqrt(lim),x^(k^2));
%o A192336   for(n=5,lim,if(polcoeff(A,n),listput(v,n)));
%o A192336   Vec(v)
%o A192336 };
%o A192336 (Python)
%o A192336 from itertools import combinations
%o A192336 def aupto(lim):
%o A192336   s = [i*i for i in range(1, int(lim**.5)+2) if i*i <= lim]
%o A192336   ss = set(sum(c) for i in range(2, len(s)+1) for c in combinations(s, i))
%o A192336   return sorted(filter(lambda x: x <= lim, ss))
%o A192336 print(aupto(104)) # _Michael S. Branicky_, May 10 2021
%Y A192336 Complement of A028237; subset of A003995.
%K A192336 nonn,easy
%O A192336 1,1
%A A192336 _Charles R Greathouse IV_, Jun 28 2011