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A344730 Numbers that are the sum of three fourth powers in exactly seven ways.

%I A344730 #10 Jul 31 2021 22:17:25
%S A344730 779888018,12478208288,33038379458,63170929458,114872872562,
%T A344730 199651332608,329296962722,393006728738,419200136082,487430011250,
%U A344730 528614071328,959702600738,1010734871328,1369390032738,1502549262242,1525400097858,1653983981762,1668273965442,1756039197458,1793250582818,1837965960992,1912768493202
%N A344730 Numbers that are the sum of three fourth powers in exactly seven ways.
%C A344730 Differs from A344729 at term 2 because 5745705602 3^4+ 230^4+ 233^4 = 25^4+ 218^4+ 243^4 = 43^4+ 207^4+ 250^4 = 58^4+ 197^4+ 255^4 = 85^4+ 177^4+ 262^4 = 90^4+ 173^4+ 263^4 = 102^4+ 163^4+ 265^4 = 122^4+ 145^4+ 267^4
%H A344730 Sean A. Irvine, <a href="/A344730/b344730.txt">Table of n, a(n) for n = 1..86</a>
%e A344730 779888018 is a term because 779888018 = 3^4+ 139^4+ 142^4 = 9^4+ 38^4+ 167^4 = 14^4+ 133^4+ 147^4 = 43^4+ 114^4+ 157^4 = 47^4+ 111^4+ 158^4 = 63^4+ 98^4+ 161^4 = 73^4+ 89^4+ 162^4
%o A344730 (Python)
%o A344730 from itertools import combinations_with_replacement as cwr
%o A344730 from collections import defaultdict
%o A344730 keep = defaultdict(lambda: 0)
%o A344730 power_terms = [x**4 for x in range(1, 1000)]
%o A344730 for pos in cwr(power_terms, 3):
%o A344730     tot = sum(pos)
%o A344730     keep[tot] += 1
%o A344730 rets = sorted([k for k, v in keep.items() if v == 7])
%o A344730 for x in range(len(rets)):
%o A344730     print(rets[x])
%Y A344730 Cf. A344648, A344729, A344738, A344923, A345085.
%K A344730 nonn
%O A344730 1,1
%A A344730 _David Consiglio, Jr._, May 27 2021