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%I #55 Sep 21 2019 02:57:17
%S 2,8,18,32,72,98,128,162,242,288,392,512,648,722,882,968,1058,1152,
%T 1458,1568,1922,2048,2178,2592,2888,3528,3698,3872,4232,4418,4608,
%U 4802,5832,6272,6498,6962,7688,7938,8192
%N Numbers n such that n^3 is the sum of two nonzero squares in exactly one way.
%C m is a term if and only if m = 2^(2a_0+1)*p_1^(2a_1)*p_2^(2a_2)*...*p_k^(2a_k), where a_i are nonnegative integers and p_i are primes of the form 4k+3. - _Chai Wah Wu_, Feb 27 2016
%C m is a term if and only if for all odd q > 1, m^q is the sum of two nonzero squares in exactly one way. - _Chai Wah Wu_, Feb 28 2016
%C Numbers n such that n is the sum of two nonzero squares while n^2 is not. - _Altug Alkan_, Apr 11 2016
%H Chai Wah Wu, <a href="/A050804/b050804.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F n such that A084888(n) = 1.
%e E.g. 32^3 = 128^2 + 128^2. Is there an example using different squares?
%e No: If n^3 has only one representation as n^3 = a^2+b^2 with 0<a<=b, then a=b. - _Jonathan Vos Post_, Feb 02 2011
%t ok[n_] := Length @ Cases[ PowersRepresentations[n^3, 2, 2], {_?Positive, _?Positive}] == 1; Select[Range[8200], ok] (* _Jean-François Alcover_, Apr 05 2011 *)
%o (Haskell)
%o a050804 n = a050804_list !! (n-1)
%o a050804_list = filter ((== 1) . a084888) [0..]
%o -- _Reinhard Zumkeller_, Jul 18 2012
%o (Python)
%o from sympy import factorint
%o A050804_list = [2*i for i in range(1,10**6) if not any(p % 4 == 1 or factorint(i)[p] % 2 for p in factorint(i))] # _Chai Wah Wu_, Feb 27 2016
%Y Cf. A000404, A050803.
%Y Cf. A081324.
%K nonn,nice
%O 1,1
%A _Patrick De Geest_, Sep 15 1999
%E More terms from _Michel ten Voorde_ and _Jud McCranie_
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