cp's OEIS Frontend

A346353 Numbers that are the sum of ten fifth powers in exactly eight ways.

%I A346353 #6 Jul 31 2021 18:54:23
%S A346353 944383,953139,953414,985453,1118585,1151438,1185375,1198879,1206546,
%T A346353 1209912,1216569,1217172,1218912,1223321,1225398,1234631,1241834,
%U A346353 1251195,1251406,1252123,1259685,1265563,1265594,1267937,1275375,1281736,1295418,1297697,1298088
%N A346353 Numbers that are the sum of ten fifth powers in exactly eight ways.
%C A346353 Differs from A345640 at term 8 because 1192180 = 5^5 + 5^5 + 5^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 10^5 + 16^5 = 2^5 + 5^5 + 5^5 + 5^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 16^5 = 3^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 6^5 + 8^5 + 13^5 + 15^5 = 3^5 + 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 7^5 + 7^5 + 13^5 + 15^5 = 2^5 + 2^5 + 2^5 + 3^5 + 8^5 + 8^5 + 9^5 + 9^5 + 12^5 + 15^5 = 1^5 + 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 12^5 + 13^5 + 13^5 = 1^5 + 2^5 + 2^5 + 2^5 + 4^5 + 11^5 + 11^5 + 12^5 + 12^5 + 13^5 = 6^5 + 9^5 + 9^5 + 10^5 + 11^5 + 11^5 + 11^5 + 11^5 + 11^5 + 11^5.
%H A346353 Sean A. Irvine, <a href="/A346353/b346353.txt">Table of n, a(n) for n = 1..10000</a>
%e A346353 944383 is a term because 944383 = 4^5 + 4^5 + 4^5 + 6^5 + 7^5 + 8^5 + 8^5 + 8^5 + 9^5 + 15^5 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 + 10^5 + 12^5 + 14^5 = 2^5 + 4^5 + 5^5 + 5^5 + 7^5 + 7^5 + 7^5 + 10^5 + 12^5 + 14^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 1^5 + 3^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 10^5 + 11^5 + 11^5 + 12^5 + 12^5.
%o A346353 (Python)
%o A346353 from itertools import combinations_with_replacement as cwr
%o A346353 from collections import defaultdict
%o A346353 keep = defaultdict(lambda: 0)
%o A346353 power_terms = [x**5 for x in range(1, 1000)]
%o A346353 for pos in cwr(power_terms, 10):
%o A346353     tot = sum(pos)
%o A346353     keep[tot] += 1
%o A346353     rets = sorted([k for k, v in keep.items() if v == 8])
%o A346353     for x in range(len(rets)):
%o A346353         print(rets[x])
%Y A346353 Cf. A345640, A345860, A346343, A346352, A346354.
%K A346353 nonn
%O A346353 1,1
%A A346353 _David Consiglio, Jr._, Jul 13 2021