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A345558 Numbers that are the sum of ten cubes in ten or more ways.

%I A345558 #6 Aug 05 2021 15:17:09
%S A345558 721,754,756,771,782,792,797,806,808,819,832,834,845,847,848,850,860,
%T A345558 862,867,869,871,874,876,877,878,881,884,886,888,893,895,897,902,903,
%U A345558 904,906,907,909,910,911,912,914,916,917,918,919,921,923,925,929,930,932
%N A345558 Numbers that are the sum of ten cubes in ten or more ways.
%H A345558 Sean A. Irvine, <a href="/A345558/b345558.txt">Table of n, a(n) for n = 1..10000</a>
%e A345558 754 is a term because 754 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 3^3 + 4^3 + 5^3 + 6^3 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3 + 5^3 = 1^3 + 1^3 + 1^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 6^3 = 1^3 + 1^3 + 2^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 5^3 + 5^3 = 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 4^3 + 4^3 + 6^3 = 1^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 5^3 + 5^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 5^3 + 6^3 = 2^3 + 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 7^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3 + 4^3 + 4^3 + 4^3 + 4^3.
%o A345558 (Python)
%o A345558 from itertools import combinations_with_replacement as cwr
%o A345558 from collections import defaultdict
%o A345558 keep = defaultdict(lambda: 0)
%o A345558 power_terms = [x**3 for x in range(1, 1000)]
%o A345558 for pos in cwr(power_terms, 10):
%o A345558     tot = sum(pos)
%o A345558     keep[tot] += 1
%o A345558     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345558     for x in range(len(rets)):
%o A345558         print(rets[x])
%Y A345558 Cf. A345549, A345557, A345603, A345812, A346808.
%K A345558 nonn
%O A345558 1,1
%A A345558 _David Consiglio, Jr._, Jun 20 2021