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A345541 Numbers that are the sum of nine cubes in two or more ways.

%I A345541 #6 Aug 05 2021 15:18:59
%S A345541 72,133,140,147,159,161,166,168,175,182,185,187,189,194,196,198,201,
%T A345541 203,205,208,213,217,220,222,224,227,231,238,239,243,245,246,250,252,
%U A345541 257,259,261,264,265,266,271,273,276,278,280,283,285,287,289,290,292,294
%N A345541 Numbers that are the sum of nine cubes in two or more ways.
%H A345541 Sean A. Irvine, <a href="/A345541/b345541.txt">Table of n, a(n) for n = 1..10000</a>
%e A345541 133 is a term because 133 = 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 4^3 = 1^3 + 1^3 + 2^3 + 2^3 + 2^3 + 2^3 + 2^3 + 3^3 + 3^3.
%o A345541 (Python)
%o A345541 from itertools import combinations_with_replacement as cwr
%o A345541 from collections import defaultdict
%o A345541 keep = defaultdict(lambda: 0)
%o A345541 power_terms = [x**3 for x in range(1, 1000)]
%o A345541 for pos in cwr(power_terms, 9):
%o A345541     tot = sum(pos)
%o A345541     keep[tot] += 1
%o A345541     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345541     for x in range(len(rets)):
%o A345541         print(rets[x])
%Y A345541 Cf. A003332, A345499, A345532, A345542, A345550, A345586, A345794.
%K A345541 nonn
%O A345541 1,1
%A A345541 _David Consiglio, Jr._, Jun 20 2021