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A343702 Numbers that are the sum of five positive cubes in two or more ways.

%I A343702 #16 May 10 2024 08:50:20
%S A343702 157,220,227,246,253,260,267,279,283,286,305,316,323,342,344,361,368,
%T A343702 377,379,384,403,410,435,440,442,468,475,487,494,501,523,530,531,549,
%U A343702 562,568,586,592,594,595,599,602,621,625,640,647,657,658,683,703,710,712,719,729,731,738,745,752,759,764,766,771,773,778,785
%N A343702 Numbers that are the sum of five positive cubes in two or more ways.
%C A343702 This sequence differs from A048927:
%C A343702 766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3
%C A343702     = 1^3 + 4^3 + 4^3 + 5^3 + 8^3
%C A343702     = 2^3 + 2^3 + 4^3 + 7^3 + 7^3.
%C A343702 So 766 is a term, but not a term of A048927.
%H A343702 David Consiglio, Jr., <a href="/A343702/b343702.txt">Table of n, a(n) for n = 1..20000</a>
%e A343702 227 = 1^3 + 1^3 + 1^3 + 2^3 + 6^3
%e A343702     = 2^3 + 3^3 + 4^3 + 4^3 + 4^3
%e A343702 so 227 is a term of this sequence.
%t A343702 Select[Range@1000,Length@Select[PowersRepresentations[#,5,3],FreeQ[#,0]&]>1&] (* _Giorgos Kalogeropoulos_, Apr 26 2021 *)
%o A343702 (Python)
%o A343702 from itertools import combinations_with_replacement as cwr
%o A343702 from collections import defaultdict
%o A343702 keep = defaultdict(lambda: 0)
%o A343702 power_terms = [x**3 for x in range(1,50)]#n
%o A343702 for pos in cwr(power_terms,5):#m
%o A343702     tot = sum(pos)
%o A343702     keep[tot] += 1
%o A343702 rets = sorted([k for k,v in keep.items() if v >= 2])#s
%o A343702 for x in range(len(rets)):
%o A343702     print(rets[x])
%Y A343702 Cf. A003328, A025406, A048927, A343704, A344238, A344795, A345511.
%K A343702 nonn,easy
%O A343702 1,1
%A A343702 _David Consiglio, Jr._, Apr 26 2021