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%I #24 Mar 17 2018 04:11:27
%S 14,21,26,29,30,35,42,45,46,49,50,53,56,61,65,70,78,84,91,93,104,106,
%T 109,115,116,120,133,140,142,145,157,168,169,180,184,190,196,200,202,
%U 205,212,224,235,244,253,260,265
%N Numbers that have a unique representation as a sum of three nonzero squares, and furthermore in this representation the squares are distinct.
%C 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.
%H Andreas Boe, <a href="/A274226/b274226.txt">Table of n, a(n) for n = 1..373</a>
%H Andreas Boe, <a href="/A274226/a274226.txt">List of values with values of x, y and z</a>
%e 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.
%e 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.
%t rp[n_] := Flatten@ IntegerPartitions[n, {3}, Range[Sqrt@n]^2]; Select[
%t Range[265], Length[u = rp[#]] == 3 && Union[u] == Sort[u] &] (* _Giovanni Resta_, Jun 15 2016 *)
%Y Cf. A025339, A004432, A274227 (the primes in this sequence).
%K nonn
%O 1,1
%A _Andreas Boe_, Jun 14 2016