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A343708 Numbers that are the sum of two positive cubes in exactly two ways.

%I A343708 #18 Jul 31 2021 23:46:43
%S A343708 1729,4104,13832,20683,32832,39312,40033,46683,64232,65728,110656,
%T A343708 110808,134379,149389,165464,171288,195841,216027,216125,262656,
%U A343708 314496,320264,327763,373464,402597,439101,443889,513000,513856,515375,525824,558441,593047,684019,704977,805688,842751,885248,886464
%N A343708 Numbers that are the sum of two positive cubes in exactly two ways.
%C A343708 This sequence differs from A001235 at term 455 because 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3 = A011541(3). Thus, this term is not in this sequence but is in A001235.
%H A343708 David Consiglio, Jr., <a href="/A343708/b343708.txt">Table of n, a(n) for n = 1..1000</a>
%e A343708 13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.
%t A343708 Select[Range@70000,Length@Select[PowersRepresentations[#,2,3],FreeQ[#,0]&]==2&] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)
%o A343708 (Python)
%o A343708 from itertools import combinations_with_replacement as cwr
%o A343708 from collections import defaultdict
%o A343708 keep = defaultdict(lambda: 0)
%o A343708 power_terms = [x**3 for x in range(1,1000)]#n
%o A343708 for pos in cwr(power_terms,2):#m
%o A343708     tot = sum(pos)
%o A343708     keep[tot] += 1
%o A343708 rets = sorted([k for k,v in keep.items() if v == 2])#s
%o A343708 for x in range(len(rets)):
%o A343708     print(rets[x])
%Y A343708 Cf. A001235, A025285, A025396, A338667, A344804.
%K A343708 nonn,easy
%O A343708 1,1
%A A343708 _David Consiglio, Jr._, Apr 26 2021