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A344943 Numbers that are the sum of five fourth powers in exactly seven ways.

%I A344943 #7 Jul 31 2021 22:03:06
%S A344943 197779,211059,217154,236675,431155,444019,480739,503539,530659,
%T A344943 548994,564979,568450,571539,602450,602770,621859,625635,625939,
%U A344943 626194,650659,651954,653059,654130,666739,687314,692754,692899,698019,708499,716739,728914,730914
%N A344943 Numbers that are the sum of five fourth powers in exactly seven ways.
%C A344943 Differs from A344942 at term 10 because 534130 = 1^4 + 3^4 + 16^4 + 22^4 + 22^4  = 2^4 + 2^4 + 4^4 + 7^4 + 27^4  = 2^4 + 3^4 + 6^4 + 6^4 + 27^4  = 2^4 + 6^4 + 9^4 + 21^4 + 24^4  = 4^4 + 16^4 + 17^4 + 18^4 + 23^4  = 6^4 + 8^4 + 11^4 + 22^4 + 23^4  = 7^4 + 8^4 + 16^4 + 19^4 + 24^4  = 13^4 + 14^4 + 14^4 + 21^4 + 22^4.
%H A344943 David Consiglio, Jr., <a href="/A344943/b344943.txt">Table of n, a(n) for n = 1..10000</a>
%e A344943 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 A344943 (Python)
%o A344943 from itertools import combinations_with_replacement as cwr
%o A344943 from collections import defaultdict
%o A344943 keep = defaultdict(lambda: 0)
%o A344943 power_terms = [x**4 for x in range(1, 1000)]
%o A344943 for pos in cwr(power_terms, 5):
%o A344943     tot = sum(pos)
%o A344943     keep[tot] += 1
%o A344943 rets = sorted([k for k, v in keep.items() if v == 7])
%o A344943 for x in range(len(rets)):
%o A344943     print(rets[x])
%Y A344943 Cf. A344923, A344941, A344942, A344945, A345181, A345819.
%K A344943 nonn
%O A344943 1,1
%A A344943 _David Consiglio, Jr._, Jun 03 2021