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A346360 Numbers that are the sum of six fifth powers in exactly five ways.

%I A346360 #6 Jul 31 2021 19:24:20
%S A346360 54827300,74115800,74883600,75609125,113088250,120274275,166078869,
%T A346360 169692136,174781858,178736448,182341225,185558208,194939538,
%U A346360 203054589,218814275,235067008,250989825,251772882,252721458,255453233,258124975,274616694,282859667,287677700
%N A346360 Numbers that are the sum of six fifth powers in exactly five ways.
%C A346360 Differs from A345719 at term 25 because 287718651 = 10^5 + 11^5 + 20^5 + 22^5 + 30^5 + 48^5 = 8^5 + 10^5 + 21^5 + 27^5 + 27^5 + 48^5 = 3^5 + 6^5 + 25^5 + 30^5 + 30^5 + 47^5 = 9^5 + 10^5 + 13^5 + 26^5 + 37^5 + 46^5 = 6^5 + 9^5 + 14^5 + 31^5 + 35^5 + 46^5 = 10^5 + 11^5 + 12^5 + 23^5 + 41^5 + 44^5.
%H A346360 Sean A. Irvine, <a href="/A346360/b346360.txt">Table of n, a(n) for n = 1..1000</a>
%e A346360 54827300 is a term because 54827300 = 4^5 + 7^5 + 21^5 + 22^5 + 23^5 + 33^5 = 5^5 + 10^5 + 15^5 + 20^5 + 28^5 + 32^5 = 1^5 + 14^5 + 16^5 + 19^5 + 28^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 29^5 + 31^5 = 5^5 + 6^5 + 19^5 + 20^5 + 29^5 + 31^5.
%o A346360 (Python)
%o A346360 from itertools import combinations_with_replacement as cwr
%o A346360 from collections import defaultdict
%o A346360 keep = defaultdict(lambda: 0)
%o A346360 power_terms = [x**5 for x in range(1, 1000)]
%o A346360 for pos in cwr(power_terms, 6):
%o A346360     tot = sum(pos)
%o A346360     keep[tot] += 1
%o A346360     rets = sorted([k for k, v in keep.items() if v == 5])
%o A346360     for x in range(len(rets)):
%o A346360         print(rets[x])
%Y A346360 Cf. A345719, A345817, A346257, A346282, A346359, A346361.
%K A346360 nonn
%O A346360 1,1
%A A346360 _David Consiglio, Jr._, Jul 13 2021