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

91, 104, 115, 119, 124, 130, 131, 136, 139, 143, 146, 147, 151, 152, 154, 155, 156, 159, 160, 163, 164, 166, 167, 168, 169, 170, 171, 175, 176, 178, 179, 180, 181, 182, 184, 187, 188, 190, 191, 192, 194, 195, 196, 199, 200, 201, 202, 203, 204, 206, 207, 208

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 = 91 = A000330(6);
a(2) = 1 + 4 + 9 + 16 + 25 + 49 = 104;
a(3) = 1 + 4 + 9 + 16 + 36 + 49 = 115;
a(4) = 1 + 4 + 9 + 16 + 25 + 64 = 119;
a(5) = 1 + 4 + 9 + 25 + 36 + 49 = 124.

Mathematica

nmax = 1000;
S[n_] := S[n] = Union[Total /@ Subsets[
     Range[Floor[Sqrt[n]]]^2, {6}]][[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)
a224981 n = a224981_list !! (n-1)
a224981_list = filter (p 6 $ 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, A224982, A224983, A000290.

Sequence in context: A344801 A184034 A294742 * A261260 A161945 A140389

Adjacent sequences: A224978 A224979 A224980 * A224982 A224983 A224984

Keyword

nonn

Author

Reinhard Zumkeller, Apr 22 2013

Status

approved