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A345087 Numbers that are the sum of three third powers in eight or more ways.

%I A345087 #8 Aug 05 2021 15:29:21
%S A345087 2562624,5618250,6525000,6755328,7374375,12742920,13581352,14027112,
%T A345087 14288373,14926248,16819704,18443160,20168784,20500992,22783032,
%U A345087 23113728,25305048,26936064,27131840,29515968,30205440,32835375,34012224,38269440,39317832,39339000
%N A345087 Numbers that are the sum of three third powers in eight or more ways.
%H A345087 David Consiglio, Jr., <a href="/A345087/b345087.txt">Table of n, a(n) for n = 1..100</a>
%e A345087 2562624 is a term because 2562624 = 7^3 + 35^3 + 135^3  = 7^3 + 63^3 + 131^3  = 11^3 + 99^3 + 115^3  = 16^3 + 45^3 + 134^3  = 29^3 + 102^3 + 112^3  = 35^3 + 59^3 + 131^3  = 50^3 + 84^3 + 121^3  = 68^3 + 71^3 + 122^3.
%o A345087 (Python)
%o A345087 from itertools import combinations_with_replacement as cwr
%o A345087 from collections import defaultdict
%o A345087 keep = defaultdict(lambda: 0)
%o A345087 power_terms = [x**3 for x in range(1, 1000)]
%o A345087 for pos in cwr(power_terms, 3):
%o A345087     tot = sum(pos)
%o A345087     keep[tot] += 1
%o A345087 rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345087 for x in range(len(rets)):
%o A345087     print(rets[x])
%Y A345087 Cf. A025336, A344737, A345086, A345088, A345119, A345152.
%K A345087 nonn
%O A345087 1,1
%A A345087 _David Consiglio, Jr._, Jun 07 2021