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%I #6 Jul 31 2021 18:29:18
%S 779888018,5745705602,8185089458,11054952818,12478208288,14355295682,
%T 21789116258,22247419922,26839201298,29428835618,31861462178,
%U 33038379458,37314202562,38214512882,41923075922,46543615202,49511121842,51711350418,54438780578,56255300738,59223741122,62862779042,63170929458,63429959138,71035097042,71447292098,73526154338,73665805122,81629817458
%N Numbers that are the sum of three fourth powers in seven or more ways.
%H David Consiglio, Jr., <a href="/A344729/b344729.txt">Table of n, a(n) for n = 1..100</a>
%e 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 (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**4 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 3):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v >= 7])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A344647, A344730, A344737, A344922, A345086.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, May 27 2021
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