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Numbers that are the sum of five positive cubes in two or more ways.
7

%I #16 May 10 2024 08:50:20

%S 157,220,227,246,253,260,267,279,283,286,305,316,323,342,344,361,368,

%T 377,379,384,403,410,435,440,442,468,475,487,494,501,523,530,531,549,

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

%C This sequence differs from A048927:

%C 766 = 1^3 + 1^3 + 2^3 + 3^3 + 9^3

%C = 1^3 + 4^3 + 4^3 + 5^3 + 8^3

%C = 2^3 + 2^3 + 4^3 + 7^3 + 7^3.

%C So 766 is a term, but not a term of A048927.

%H David Consiglio, Jr., <a href="/A343702/b343702.txt">Table of n, a(n) for n = 1..20000</a>

%e 227 = 1^3 + 1^3 + 1^3 + 2^3 + 6^3

%e = 2^3 + 3^3 + 4^3 + 4^3 + 4^3

%e so 227 is a term of this sequence.

%t Select[Range@1000,Length@Select[PowersRepresentations[#,5,3],FreeQ[#,0]&]>1&] (* _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(1,50)]#n

%o for pos in cwr(power_terms,5):#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. A003328, A025406, A048927, A343704, A344238, A344795, A345511.

%K nonn,easy

%O 1,1

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