cp's OEIS Frontend

A346350 Numbers that are the sum of ten fifth powers in exactly five ways.

%I A346350 #6 Jul 31 2021 18:54:12
%S A346350 200009,220350,235658,329271,329810,330052,359211,359453,359498,
%T A346350 360298,367314,368529,374519,374847,375089,375870,376620,376651,
%U A346350 377159,377643,380283,382622,384395,384934,387035,388933,391736,392064,392275,392339,392517,392581
%N A346350 Numbers that are the sum of ten fifth powers in exactly five ways.
%C A346350 Differs from A345637 at term 29 because 392095 = 2^5 + 2^5 + 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 1^5 + 1^5 + 1^5 + 5^5 + 6^5 + 6^5 + 6^5 + 7^5 + 10^5 + 12^5 = 2^5 + 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 2^5 + 2^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 1^5 + 1^5 + 1^5 + 2^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5.
%H A346350 Sean A. Irvine, <a href="/A346350/b346350.txt">Table of n, a(n) for n = 1..10000</a>
%e A346350 200009 is a term because 200009 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 6^5 + 6^5 + 9^5 + 10^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 8^5 + 10^5 = 1^5 + 3^5 + 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 8^5 + 10^5 = 2^5 + 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 8^5 + 8^5 + 9^5 = 1^5 + 2^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5.
%o A346350 (Python)
%o A346350 from itertools import combinations_with_replacement as cwr
%o A346350 from collections import defaultdict
%o A346350 keep = defaultdict(lambda: 0)
%o A346350 power_terms = [x**5 for x in range(1, 1000)]
%o A346350 for pos in cwr(power_terms, 10):
%o A346350     tot = sum(pos)
%o A346350     keep[tot] += 1
%o A346350     rets = sorted([k for k, v in keep.items() if v == 5])
%o A346350     for x in range(len(rets)):
%o A346350         print(rets[x])
%Y A346350 Cf. A345637, A345857, A346340, A346349, A346351.
%K A346350 nonn
%O A346350 1,1
%A A346350 _David Consiglio, Jr._, Jul 13 2021