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
Keywords
Examples
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.
Links
- Andreas Boe, Table of n, a(n) for n = 1..373
- Andreas Boe, List of values with values of x, y and z
Programs
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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 *)
Comments