A245022 Integers with precisely three partitions into sums of four squares of nonnegative numbers.

18, 25, 26, 27, 28, 33, 37, 38, 41, 43, 51, 53, 55, 59, 60, 62, 72, 79, 92, 95, 104, 112, 152, 240, 248, 288, 368, 416, 448, 608, 960, 992, 1152, 1472, 1664, 1792, 2432, 3840, 3968, 4608, 5888, 6656, 7168, 9728, 15360, 15872, 18432, 23552, 26624, 28672

Offset

1,1

Comments

A002635(a(n)) = 3.

Links

Robert Price, Table of n, a(n) for n = 1..55

Index entries for sequences related to sums of squares

Example

a(1) = 18 = 16 + 1 + 1 + 0 = 9 + 9 + 0 + 0 = 9 + 4 + 4 + 1;
a(2) = 25 = 25 + 0 + 0 + 0 = 16 + 9 + 0 + 0 = 16 + 4 + 4 + 1;
a(3) = 26 = 25 + 1 + 0 + 0 = 16 + 9 + 1 + 0 = 9 + 9 + 4 + 4;
a(4) = 27 = 25 + 1 + 1 + 0 = 16 + 9 + 1 + 1 = 9 + 9 + 9 + 0;
a(5) = 28 = 25 + 1 + 1 + 1 = 16 + 4 + 4 + 4 = 9 + 9 + 9 + 1;
a(6) = 33 = 25 + 4 + 4 + 0 = 16 + 16 + 1 + 0 = 16 + 9 + 4 + 4;
a(7) = 37 = 36 + 1 + 0 + 0 = 25 + 4 + 4 + 4 = 16 + 16 + 4 + 1;
a(8) = 38 = 36 + 1 + 1 + 0 = 25 + 9 + 4 + 0 = 16 + 9 + 9 + 4;
a(9) = 41 = 36 + 4 + 1 + 0 = 25 + 16 + 0 + 0 = 16 + 16 + 9 + 0;
a(10) = 43 = 25 + 16 + 1 + 1 = 25 + 9 + 9 + 0 = 16 + 9 + 9 + 9;
a(11) = 51 = 49 + 1 + 1 + 0 = 25 + 25 + 1 + 0 = 25 + 16 + 9 + 1;
a(12) = 53 = 49 + 4 + 0 + 0 = 36 + 16 + 1 + 0 = 36 + 9 + 4 + 4.

Mathematica

Select[ Range@ 30000, Length@PowersRepresentations[#, 4, 2] == 3 &] (* Robert G. Wilson v, Oct 27 2017 *)

Prog

(Haskell)
a245022 n = a245022_list !! (n-1)
a245022_list = filter ((== 3) . a002635) [0..]

Crossrefs

Cf. A002635, A006431, A180149.

Sequence in context: A166471 A072422 A003300 * A362435 A248111 A109769

Adjacent sequences: A245019 A245020 A245021 * A245023 A245024 A245025

Keyword

nonn

Author

Reinhard Zumkeller, Jul 13 2014

Extensions

a(44)-a(50) from Robert Price, Oct 26 2017

Status

approved