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A346355 Numbers that are the sum of ten fifth powers in exactly ten ways.

%I A346355 #6 Jul 31 2021 18:54:31
%S A346355 1431641,1439416,1464377,1464408,1505660,1531640,1564165,1782171,
%T A346355 1969253,1976997,1986028,2000966,2028270,2042460,2052415,2058421,
%U A346355 2059202,2060522,2076393,2130272,2201247,2208681,2209704,2248941,2250329,2251042,2282073,2307747,2315379
%N A346355 Numbers that are the sum of ten fifth powers in exactly ten ways.
%C A346355 Differs from A345642 at term 6 because 1531398 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 10^5 + 12^5 + 16^5 = 1^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 10^5 + 11^5 + 11^5 + 16^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 10^5 + 14^5 + 15^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 10^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 4^5 + 10^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 + 13^5 + 14^5 + 14^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 13^5 + 14^5 + 14^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 13^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 7^5 + 7^5 + 10^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 10^5 + 12^5 + 12^5 + 13^5 + 14^5.
%H A346355 Sean A. Irvine, <a href="/A346355/b346355.txt">Table of n, a(n) for n = 1..10000</a>
%e A346355 1431641 is a term because 1431641 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 1^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 1^5 + 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 1^5 + 1^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 3^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 3^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.
%o A346355 (Python)
%o A346355 from itertools import combinations_with_replacement as cwr
%o A346355 from collections import defaultdict
%o A346355 keep = defaultdict(lambda: 0)
%o A346355 power_terms = [x**5 for x in range(1, 1000)]
%o A346355 for pos in cwr(power_terms, 10):
%o A346355     tot = sum(pos)
%o A346355     keep[tot] += 1
%o A346355     rets = sorted([k for k, v in keep.items() if v == 10])
%o A346355     for x in range(len(rets)):
%o A346355         print(rets[x])
%Y A346355 Cf. A345642, A345862, A346345, A346354.
%K A346355 nonn
%O A346355 1,1
%A A346355 _David Consiglio, Jr._, Jul 13 2021