cp's OEIS Frontend

A346354 Numbers that are the sum of ten fifth powers in exactly nine ways.

%I A346354 #6 Jul 31 2021 18:54:27
%S A346354 1192180,1226654,1242437,1431399,1431430,1431672,1431883,1432453,
%T A346354 1432664,1434765,1439174,1441695,1442718,1447602,1448447,1455346,
%U A346354 1455377,1464166,1474431,1474462,1475485,1491978,1497619,1531429,1539173,1614736,1671199,1671410,1672937
%N A346354 Numbers that are the sum of ten fifth powers in exactly nine ways.
%C A346354 Differs from A345641 at term 6 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.
%H A346354 Sean A. Irvine, <a href="/A346354/b346354.txt">Table of n, a(n) for n = 1..10000</a>
%e A346354 1192180 is a term 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.
%o A346354 (Python)
%o A346354 from itertools import combinations_with_replacement as cwr
%o A346354 from collections import defaultdict
%o A346354 keep = defaultdict(lambda: 0)
%o A346354 power_terms = [x**5 for x in range(1, 1000)]
%o A346354 for pos in cwr(power_terms, 10):
%o A346354     tot = sum(pos)
%o A346354     keep[tot] += 1
%o A346354     rets = sorted([k for k, v in keep.items() if v == 9])
%o A346354     for x in range(len(rets)):
%o A346354         print(rets[x])
%Y A346354 Cf. A345641, A345861, A346344, A346353, A346355.
%K A346354 nonn
%O A346354 1,1
%A A346354 _David Consiglio, Jr._, Jul 13 2021