A343708 - OEIS

%I #18 Jul 31 2021 23:46:43

%S 1729,4104,13832,20683,32832,39312,40033,46683,64232,65728,110656,

%T 110808,134379,149389,165464,171288,195841,216027,216125,262656,

%U 314496,320264,327763,373464,402597,439101,443889,513000,513856,515375,525824,558441,593047,684019,704977,805688,842751,885248,886464

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

%C 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 David Consiglio, Jr., <a href="/A343708/b343708.txt">Table of n, a(n) for n = 1..1000</a>

%e 13832 is in this sequence because 13832 = 2^3 + 24^3 = 18^3 + 20^3.

%t Select[Range@70000,Length@Select[PowersRepresentations[#,2,3],FreeQ[#,0]&]==2&] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**3 for x in range(1,1000)]#n

%o for pos in cwr(power_terms,2):#m

%o     tot = sum(pos)

%o     keep[tot] += 1

%o rets = sorted([k for k,v in keep.items() if v == 2])#s

%o for x in range(len(rets)):

%o     print(rets[x])

%Y Cf. A001235, A025285, A025396, A338667, A344804.

%K nonn,easy

%O 1,1

%A _David Consiglio, Jr._, Apr 26 2021