cp's OEIS Frontend

A346345 Numbers that are the sum of nine fifth powers in exactly ten ways.

%I A346345 #6 Jul 31 2021 19:01:16
%S A346345 4157156,4492410,4510461,4915538,5005474,5015506,5179747,5219655,
%T A346345 5756794,6323426,6326519,6382443,6423394,6705284,6793170,6861218,
%U A346345 7101038,7147645,7147656,7148679,7266240,7280391,7283268,7314187,7413493,7422352,7531076,7651645,7693425
%N A346345 Numbers that are the sum of nine fifth powers in exactly ten ways.
%C A346345 Differs from A345627 at term 5 because 4948274 = 2^5 + 4^5 + 4^5 + 5^5 + 6^5 + 8^5 + 9^5 + 15^5 + 21^5 = 1^5 + 3^5 + 5^5 + 5^5 + 8^5 + 8^5 + 8^5 + 15^5 + 21^5 = 1^5 + 2^5 + 2^5 + 5^5 + 5^5 + 11^5 + 11^5 + 17^5 + 20^5 = 8^5 + 9^5 + 9^5 + 10^5 + 10^5 + 10^5 + 12^5 + 16^5 + 20^5 = 4^5 + 8^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 + 16^5 + 19^5 = 4^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 15^5 + 19^5 = 4^5 + 4^5 + 9^5 + 13^5 + 13^5 + 13^5 + 14^5 + 15^5 + 19^5 = 6^5 + 6^5 + 9^5 + 9^5 + 12^5 + 12^5 + 14^5 + 18^5 + 18^5 = 1^5 + 8^5 + 8^5 + 12^5 + 12^5 + 14^5 + 14^5 + 17^5 + 18^5 = 1^5 + 8^5 + 9^5 + 9^5 + 13^5 + 14^5 + 16^5 + 17^5 + 17^5 = 3^5 + 7^5 + 7^5 + 10^5 + 12^5 + 16^5 + 16^5 + 16^5 + 17^5.
%H A346345 Sean A. Irvine, <a href="/A346345/b346345.txt">Table of n, a(n) for n = 1..10000</a>
%e A346345 4157156 is a term because 4157156 = 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 9^5 + 21^5 = 1^5 + 1^5 + 3^5 + 4^5 + 5^5 + 5^5 + 8^5 + 8^5 + 21^5 = 1^5 + 4^5 + 4^5 + 8^5 + 10^5 + 12^5 + 12^5 + 16^5 + 19^5 = 1^5 + 4^5 + 4^5 + 8^5 + 8^5 + 14^5 + 14^5 + 14^5 + 19^5 = 5^5 + 5^5 + 5^5 + 5^5 + 7^5 + 9^5 + 15^5 + 17^5 + 18^5 = 3^5 + 3^5 + 5^5 + 6^5 + 9^5 + 10^5 + 16^5 + 16^5 + 18^5 = 1^5 + 1^5 + 5^5 + 5^5 + 13^5 + 13^5 + 15^5 + 15^5 + 18^5 = 2^5 + 3^5 + 4^5 + 4^5 + 10^5 + 14^5 + 16^5 + 16^5 + 17^5 = 11^5 + 11^5 + 12^5 + 12^5 + 12^5 + 12^5 + 13^5 + 16^5 + 17^5 = 2^5 + 2^5 + 2^5 + 5^5 + 12^5 + 15^5 + 16^5 + 16^5 + 16^5.
%o A346345 (Python)
%o A346345 from itertools import combinations_with_replacement as cwr
%o A346345 from collections import defaultdict
%o A346345 keep = defaultdict(lambda: 0)
%o A346345 power_terms = [x**5 for x in range(1, 1000)]
%o A346345 for pos in cwr(power_terms, 9):
%o A346345     tot = sum(pos)
%o A346345     keep[tot] += 1
%o A346345     rets = sorted([k for k, v in keep.items() if v == 10])
%o A346345     for x in range(len(rets)):
%o A346345         print(rets[x])
%Y A346345 Cf. A345627, A345852, A346335, A346344, A346355.
%K A346345 nonn
%O A346345 1,1
%A A346345 _David Consiglio, Jr._, Jul 13 2021