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A345512 Numbers that are the sum of six cubes in three or more ways.

%I A345512 #6 Aug 05 2021 15:23:50
%S A345512 221,254,369,411,443,469,495,502,576,595,600,626,648,658,684,704,711,
%T A345512 720,739,746,753,760,765,767,772,774,779,786,793,811,818,828,830,835,
%U A345512 837,844,854,856,863,866,873,874,880,884,886,891,892,893,899,905,910,919
%N A345512 Numbers that are the sum of six cubes in three or more ways.
%H A345512 Sean A. Irvine, <a href="/A345512/b345512.txt">Table of n, a(n) for n = 1..10000</a>
%e A345512 254 is a term because 254 = 1^3 + 1^3 + 1^3 + 1^3 + 4^3 + 4^3 = 1^3 + 1^3 + 1^3 + 2^3 + 3^3 + 5^3 = 2^3 + 3^3 + 3^3 + 3^3 + 3^3 + 3^3.
%o A345512 (Python)
%o A345512 from itertools import combinations_with_replacement as cwr
%o A345512 from collections import defaultdict
%o A345512 keep = defaultdict(lambda: 0)
%o A345512 power_terms = [x**3 for x in range(1, 1000)]
%o A345512 for pos in cwr(power_terms, 6):
%o A345512     tot = sum(pos)
%o A345512     keep[tot] += 1
%o A345512     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345512     for x in range(len(rets)):
%o A345512         print(rets[x])
%Y A345512 Cf. A048931, A343704, A344807, A345511, A345513, A345521, A345560.
%K A345512 nonn
%O A345512 1,1
%A A345512 _David Consiglio, Jr._, Jun 20 2021