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%I #14 May 11 2024 20:43:32
%S 2295937600,4335900525,6251954544,8986552608,13413708308,14539246326,
%T 15277569450,15728636000,16770321920,16873011232,17572402769,
%U 17713454592,17960776999,18190647200,19621666592,20570070125,20827689300,22322555200,23461554774,23613244800
%N Numbers that are the sum of six fifth powers in exactly eight ways.
%C This sequence differs from A345722:
%C 9085584992 = 24^5 + 38^5 + 42^5 + 48^5 + 54^5 + 96^5
%C = 21^5 + 34^5 + 38^5 + 43^5 + 74^5 + 92^5
%C = 8^5 + 34^5 + 38^5 + 62^5 + 68^5 + 92^5
%C = 18^5 + 18^5 + 44^5 + 64^5 + 66^5 + 92^5
%C = 13^5 + 18^5 + 51^5 + 64^5 + 64^5 + 92^5
%C = 8^5 + 38^5 + 41^5 + 47^5 + 79^5 + 89^5
%C = 5^5 + 23^5 + 29^5 + 45^5 + 85^5 + 85^5
%C = 8^5 + 23^5 + 41^5 + 64^5 + 82^5 + 84^5
%C = 12^5 + 18^5 + 38^5 + 72^5 + 78^5 + 84^5,
%C so 9085584992 is in A345722, but is not in this sequence.
%H Sean A. Irvine, <a href="/A346363/b346363.txt">Table of n, a(n) for n = 1..4934</a>
%e 2295937600 = 4^5 + 21^5 + 38^5 + 42^5 + 43^5 + 72^5
%e = 8^5 + 16^5 + 30^5 + 42^5 + 54^5 + 70^5
%e = 8^5 + 13^5 + 36^5 + 37^5 + 57^5 + 69^5
%e = 14^5 + 16^5 + 16^5 + 52^5 + 54^5 + 68^5
%e = 3^5 + 14^5 + 32^5 + 44^5 + 61^5 + 66^5
%e = 4^5 + 18^5 + 22^5 + 52^5 + 58^5 + 66^5
%e = 10^5 + 14^5 + 26^5 + 42^5 + 63^5 + 65^5
%e = 1^5 + 7^5 + 34^5 + 57^5 + 58^5 + 63^5,
%e so 2295937600 is a term.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**5 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 6):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 8])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345722, A345820, A346285, A346362, A346364.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jul 13 2021
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