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A346361 Numbers that are the sum of six fifth powers in exactly six ways.

%I A346361 #6 Jul 31 2021 19:24:24
%S A346361 287718651,553545456,746783675,972232800,1005620508,1040741042,
%T A346361 1070652352,1074892544,1182426366,1197332400,1243267146,1317183650,
%U A346361 1364866263,1387455091,1429663400,1498160992,1529189818,1554833117,1558594400,1610298901,1623782765,1627228231
%N A346361 Numbers that are the sum of six fifth powers in exactly six ways.
%C A346361 Differs from A345720 at term 10 because 1184966816 = 15^5 + 24^5 + 27^5 + 38^5 + 39^5 + 63^5 = 2^5 + 28^5 + 36^5 + 36^5 + 42^5 + 62^5 = 4^5 + 24^5 + 38^5 + 38^5 + 40^5 + 62^5 = 21^5 + 32^5 + 37^5 + 41^5 + 45^5 + 60^5 = 8^5 + 14^5 + 34^5 + 40^5 + 52^5 + 58^5 = 11^5 + 17^5 + 22^5 + 49^5 + 51^5 + 56^5 = 11^5 + 16^5 + 22^5 + 52^5 + 52^5 + 53^5.
%H A346361 Sean A. Irvine, <a href="/A346361/b346361.txt">Table of n, a(n) for n = 1..10000</a>
%e A346361 287718651 is a term 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.
%o A346361 (Python)
%o A346361 from itertools import combinations_with_replacement as cwr
%o A346361 from collections import defaultdict
%o A346361 keep = defaultdict(lambda: 0)
%o A346361 power_terms = [x**5 for x in range(1, 1000)]
%o A346361 for pos in cwr(power_terms, 6):
%o A346361     tot = sum(pos)
%o A346361     keep[tot] += 1
%o A346361     rets = sorted([k for k, v in keep.items() if v == 6])
%o A346361     for x in range(len(rets)):
%o A346361         print(rets[x])
%Y A346361 Cf. A345720, A345818, A346283, A346360, A346362.
%K A346361 nonn
%O A346361 1,1
%A A346361 _David Consiglio, Jr._, Jul 13 2021