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A224981 Numbers that are the sum of exactly 6 distinct nonzero squares.

%I A224981 #9 Nov 20 2021 09:35:19
%S A224981 91,104,115,119,124,130,131,136,139,143,146,147,151,152,154,155,156,
%T A224981 159,160,163,164,166,167,168,169,170,171,175,176,178,179,180,181,182,
%U A224981 184,187,188,190,191,192,194,195,196,199,200,201,202,203,204,206,207,208
%N A224981 Numbers that are the sum of exactly 6 distinct nonzero squares.
%H A224981 Reinhard Zumkeller, <a href="/A224981/b224981.txt">Table of n, a(n) for n = 1..1000</a>
%H A224981 Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa67/aa6745.pdf">Sums of distinct squares</a>, Acta Arithmetica 67 (1994), pp. 349-380.
%H A224981 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%e A224981 a(1) = 1 + 4 + 9 + 16 + 25 + 36 = 91 = A000330(6);
%e A224981 a(2) = 1 + 4 + 9 + 16 + 25 + 49 = 104;
%e A224981 a(3) = 1 + 4 + 9 + 16 + 36 + 49 = 115;
%e A224981 a(4) = 1 + 4 + 9 + 16 + 25 + 64 = 119;
%e A224981 a(5) = 1 + 4 + 9 + 25 + 36 + 49 = 124.
%t A224981 nmax = 1000;
%t A224981 S[n_] := S[n] = Union[Total /@ Subsets[
%t A224981      Range[Floor[Sqrt[n]]]^2, {6}]][[1 ;; nmax]];
%t A224981 S[nmax];
%t A224981 S[n = nmax + 1];
%t A224981 While[S[n] != S[n - 1], n++];
%t A224981 S[n] (* _Jean-François Alcover_, Nov 20 2021 *)
%o A224981 (Haskell)
%o A224981 a224981 n = a224981_list !! (n-1)
%o A224981 a224981_list = filter (p 6 $ tail a000290_list) [1..] where
%o A224981    p k (q:qs) m = k == 0 && m == 0 ||
%o A224981                   q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m)
%Y A224981 Cf. A003995, A004431, A004432, A004433, A004434, A224982, A224983, A000290.
%K A224981 nonn
%O A224981 1,1
%A A224981 _Reinhard Zumkeller_, Apr 22 2013