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A345550 Numbers that are the sum of ten cubes in two or more ways.

%I A345550 #6 Aug 05 2021 15:16:38
%S A345550 73,80,99,134,136,141,148,155,160,162,167,169,174,176,183,186,188,190,
%T A345550 192,193,195,197,199,202,204,206,209,211,212,213,214,216,218,221,223,
%U A345550 225,228,230,232,235,239,240,244,246,247,249,251,253,254,258,260,262
%N A345550 Numbers that are the sum of ten cubes in two or more ways.
%H A345550 Sean A. Irvine, <a href="/A345550/b345550.txt">Table of n, a(n) for n = 1..10000</a>
%e A345550 80 is a term because 80 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 2^3 + 3^3 = 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3.
%o A345550 (Python)
%o A345550 from itertools import combinations_with_replacement as cwr
%o A345550 from collections import defaultdict
%o A345550 keep = defaultdict(lambda: 0)
%o A345550 power_terms = [x**3 for x in range(1, 1000)]
%o A345550 for pos in cwr(power_terms, 10):
%o A345550     tot = sum(pos)
%o A345550     keep[tot] += 1
%o A345550     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345550     for x in range(len(rets)):
%o A345550         print(rets[x])
%Y A345550 Cf. A003333, A345509, A345541, A345551, A345595, A345804.
%K A345550 nonn
%O A345550 1,1
%A A345550 _David Consiglio, Jr._, Jun 20 2021