A274226 Numbers that have a unique representation as a sum of three nonzero squares, and furthermore in this representation the squares are distinct.

14, 21, 26, 29, 30, 35, 42, 45, 46, 49, 50, 53, 56, 61, 65, 70, 78, 84, 91, 93, 104, 106, 109, 115, 116, 120, 133, 140, 142, 145, 157, 168, 169, 180, 184, 190, 196, 200, 202, 205, 212, 224, 235, 244, 253, 260, 265

Offset

1,1

Comments

The numbers in this sequence can be expressed as a sum of 3 positive squares in exactly one way, and those 3 squares are distinct. This is different from A025339.

Links

Andreas Boe, Table of n, a(n) for n = 1..373

Andreas Boe, List of values with values of x, y and z

Example

14 is a term because it can be expressed in just one way as a sum of 3 squares (1^2+2^2+3^2) and the 3 squares are different.
38 is not a term, because, even if it can be expressed as a sum of 3 distinct squares in just one way (2^2+3^2+5^2), it can also be expressed as a sum of 3 non-distinct squares (1^2+1^2+6^2). This makes 38 a member of A004432 and A025339.

Mathematica

rp[n_] := Flatten@ IntegerPartitions[n, {3}, Range[Sqrt@n]^2]; Select[
Range[265], Length[u = rp[#]] == 3 && Union[u] == Sort[u] &] (* Giovanni Resta, Jun 15 2016 *)

Crossrefs

Cf. A025339, A004432, A274227 (the primes in this sequence).

Sequence in context: A025339 A224771 A096017 * A324073 A006614 A039832

Adjacent sequences: A274223 A274224 A274225 * A274227 A274228 A274229

Keyword

nonn

Author

Andreas Boe, Jun 14 2016

Status

approved