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A346349 Numbers that are the sum of ten fifth powers in exactly four ways.

%I A346349 #6 Jul 31 2021 18:54:08
%S A346349 55543,55574,55785,56566,58667,63318,72349,73002,85186,86506,87287,
%T A346349 87529,88310,103134,111498,113599,114591,118250,119031,120351,120382,
%U A346349 120593,121374,123475,128126,134475,134878,135201,137157,142008,142219,143000,143211,143506
%N A346349 Numbers that are the sum of ten fifth powers in exactly four ways.
%C A346349 Differs from A345636 at term 92 because 200009 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 8^5 + 10^5 = 1^5 + 3^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 8^5 + 10^5 = 2^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 = 1^5 + 2^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5.
%H A346349 Sean A. Irvine, <a href="/A346349/b346349.txt">Table of n, a(n) for n = 1..10000</a>
%e A346349 55543 is a term because 55543 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5.
%o A346349 (Python)
%o A346349 from itertools import combinations_with_replacement as cwr
%o A346349 from collections import defaultdict
%o A346349 keep = defaultdict(lambda: 0)
%o A346349 power_terms = [x**5 for x in range(1, 1000)]
%o A346349 for pos in cwr(power_terms, 10):
%o A346349     tot = sum(pos)
%o A346349     keep[tot] += 1
%o A346349     rets = sorted([k for k, v in keep.items() if v == 4])
%o A346349     for x in range(len(rets)):
%o A346349         print(rets[x])
%Y A346349 Cf. A345636, A345856, A346339, A346348, A346350.
%K A346349 nonn
%O A346349 1,1
%A A346349 _David Consiglio, Jr._, Jul 13 2021