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%I #8 Jul 31 2021 18:13:33
%S 197779,211059,217154,236675,431155,444019,480739,503539,530659,
%T 534130,548994,564979,568450,571539,602450,602770,619090,621859,
%U 625635,625939,626194,650659,651954,653059,654130,654754,663155,666739,687314,692754,692899,698019
%N Numbers that are the sum of five fourth powers in seven or more ways.
%H David Consiglio, Jr., <a href="/A344942/b344942.txt">Table of n, a(n) for n = 1..10000</a>
%e 197779 is a term because 197779 = 1^4 + 5^4 + 6^4 + 16^4 + 19^4 = 1^4 + 7^4 + 11^4 + 12^4 + 20^4 = 1^4 + 10^4 + 12^4 + 17^4 + 17^4 = 2^4 + 4^4 + 5^4 + 7^4 + 21^4 = 3^4 + 5^4 + 6^4 + 6^4 + 21^4 = 4^4 + 7^4 + 9^4 + 13^4 + 20^4 = 11^4 + 13^4 + 14^4 + 15^4 + 16^4.
%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, 5):
%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. A344922, A344940, A344943, A344944, A345180, A345564.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jun 03 2021
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