cp's OEIS Frontend

A338667 Numbers that are the sum of two positive cubes in exactly one way.

%I A338667 #26 Jul 31 2021 23:46:35
%S A338667 2,9,16,28,35,54,65,72,91,126,128,133,152,189,217,224,243,250,280,341,
%T A338667 344,351,370,407,432,468,513,520,539,559,576,637,686,728,730,737,756,
%U A338667 793,854,855,945,1001,1008,1024,1027,1064,1072,1125,1216,1241,1332,1339,1343,1358,1395,1456,1458,1512,1547,1674,1736
%N A338667 Numbers that are the sum of two positive cubes in exactly one way.
%C A338667 This sequence differs from A003325 at term 61: A003325(61) = 1729 is the famous Ramanujan taxicab number and is excluded from this sequence because it is the sum of two cubes in two distinct ways.
%H A338667 David Consiglio, Jr., <a href="/A338667/b338667.txt">Table of n, a(n) for n = 1..20000</a>
%e A338667 35 is a term of this sequence because 2^3 + 3^3 = 8 + 27 = 35 and this is the one and only way to express 35 as the sum of two cubes.
%t A338667 Select[Range@2000,Length[s=PowersRepresentations[#,2,3]]==1&&And@@(#>0&@@@s)&] (* _Giorgos Kalogeropoulos_, Apr 24 2021 *)
%o A338667 (Python)
%o A338667 from itertools import combinations_with_replacement as cwr
%o A338667 from collections import defaultdict
%o A338667 from bisect import bisect_left as bisect
%o A338667 keep = defaultdict(lambda: 0)
%o A338667 power_terms = [x**3 for x in range(1,1000)]
%o A338667 for pos in cwr(power_terms,2):
%o A338667     tot = sum(pos)
%o A338667     keep[tot] += 1
%o A338667 rets = sorted([k for k,v in keep.items() if v == 1])
%o A338667 for x in range(len(rets)):
%o A338667     print(rets[x])
%Y A338667 Cf. A003325, A025284, A025395, A343708, A344187.
%K A338667 nonn,easy
%O A338667 1,1
%A A338667 _David Consiglio, Jr._, Apr 22 2021