A224982 Numbers that are the sum of exactly 7 distinct nonzero squares.

140, 155, 168, 172, 179, 185, 188, 191, 195, 196, 200, 203, 204, 205, 211, 212, 215, 217, 219, 220, 224, 225, 227, 230, 231, 232, 233, 235, 236, 239, 240, 243, 244, 245, 246, 247, 248, 251, 252, 254, 256, 257, 259, 260, 263, 264, 265, 267, 268, 269, 270, 271

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 = 140 = A000330(7);
a(2) = 1 + 4 + 9 + 16 + 25 + 36 + 64 = 155;
a(3) = 1 + 4 + 9 + 16 + 25 + 49 + 64 = 168;
a(4) = 1 + 4 + 9 + 16 + 25 + 36 + 81 = 172;
a(5) = 1 + 4 + 9 + 16 + 36 + 49 + 64 = 179.

Mathematica

nmax = 1000;
S[n_] := S[n] = Union[Total /@ Subsets[
     Range[Floor[Sqrt[n]]]^2, {7}]][[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)
a224982 n = a224982_list !! (n-1)
a224982_list = filter (p 7 $ 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, A224983, A000290.

Sequence in context: A114825 A308617 A353074 * A256085 A054573 A131492

Adjacent sequences: A224979 A224980 A224981 * A224983 A224984 A224985

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2013

Status

approved