cp's OEIS Frontend

A345642 Numbers that are the sum of ten fifth powers in ten or more ways.

%I A345642 #6 Jul 31 2021 15:59:01
%S A345642 1431641,1439416,1464377,1464408,1505660,1531398,1531640,1564165,
%T A345642 1697929,1703935,1782171,1969222,1969253,1969464,1976997,1985183,
%U A345642 1986028,2000966,2001989,2028270,2042460,2052415,2058421,2059202,2060522,2069221,2076393,2130272,2182162
%N A345642 Numbers that are the sum of ten fifth powers in ten or more ways.
%H A345642 Sean A. Irvine, <a href="/A345642/b345642.txt">Table of n, a(n) for n = 1..1000</a>
%e A345642 1439416 is a term because 1439416 = 1^5 + 1^5 + 2^5 + 7^5 + 8^5 + 8^5 + 10^5 + 12^5 + 12^5 + 15^5 = 1^5 + 2^5 + 3^5 + 6^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 3^5 + 5^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 1^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 2^5 + 2^5 + 3^5 + 4^5 + 6^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 3^5 + 6^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 3^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 7^5 + 11^5 + 11^5 + 16^5 = 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5.
%o A345642 (Python)
%o A345642 from itertools import combinations_with_replacement as cwr
%o A345642 from collections import defaultdict
%o A345642 keep = defaultdict(lambda: 0)
%o A345642 power_terms = [x**5 for x in range(1, 1000)]
%o A345642 for pos in cwr(power_terms, 10):
%o A345642     tot = sum(pos)
%o A345642     keep[tot] += 1
%o A345642     rets = sorted([k for k, v in keep.items() if v >= 10])
%o A345642     for x in range(len(rets)):
%o A345642         print(rets[x])
%Y A345642 Cf. A345603, A345627, A345641, A346355.
%K A345642 nonn
%O A345642 1,1
%A A345642 _David Consiglio, Jr._, Jun 20 2021