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A224983 Numbers that are the sum of exactly 8 distinct nonzero squares. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Paul T. Bateman, Adolf J. Hildebrand, and George B. Purdy, Sums of distinct squares, Acta Arithmetica 67 (1994), pp. 349-380.
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
Sequence in context: A348823 A198722 A198913 * A138605 A260975 A271643
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Apr 22 2013
STATUS
approved

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Last modified February 21 22:13 EST 2024. Contains 370237 sequences. (Running on oeis4.)