A224983 Numbers that are the sum of exactly 8 distinct nonzero squares.

204, 221, 236, 240, 249, 255, 260, 261, 268, 269, 272, 276, 279, 281, 284, 285, 288, 289, 293, 295, 296, 299, 300, 303, 305, 306, 309, 311, 312, 316, 317, 320, 321, 323, 324, 325, 326, 327, 329, 332, 333, 335, 336, 337, 338, 339, 340, 341, 344, 345, 347, 348

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, Sums of distinct squares, Acta Arithmetica 67 (1994), pp. 349-380.

Index entries for sequences related to sums of squares

Example

a(1) = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204 = A000330(8);
a(2) = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 81 = 221;
a(3) = 1 + 4 + 9 + 16 + 25 + 36 + 64 + 81 = 236;
a(4) = 1 + 4 + 9 + 16 + 25 + 36 + 49 + 100 = 240;
a(5) = 1 + 4 + 9 + 16 + 25 + 49 + 64 + 81 = 249.

Mathematica

nmax = 1000;
S[n_] := S[n] = Union[Total /@ Subsets[
     Range[Floor[Sqrt[n]]]^2, {8}]][[1 ;; nmax]];
S[nmax];
S[n = nmax + 1];
While[S[n] != S[n - 1], n++];
S[n] (* Jean-François Alcover, Nov 20 2021 *)

Prog

(Haskell)
a224983 n = a224983_list !! (n-1)
a224983_list = filter (p 8 $ tail a000290_list) [1..] where
   p k (q:qs) m = k == 0 && m == 0 ||
                  q <= m && k >= 0 && (p (k - 1) qs (m - q) || p k qs m)

Crossrefs

Cf. A003995, A004431, A004432, A004433, A004434, A224981, A224982, A000290.

Sequence in context: A348823 A198722 A198913 * A138605 A260975 A271643

Adjacent sequences: A224980 A224981 A224982 * A224984 A224985 A224986

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2013

Status

approved