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%I #6 Jul 31 2021 19:11:49
%S 4099,4130,4161,4341,4372,4583,5122,5153,5364,6145,7223,7254,7465,
%T 8246,10347,11874,11905,12116,12897,14998,19649,20905,20936,21147,
%U 21928,24029,28680,36866,36897,37108,37711,37889,39990,40138,44641,51393,51448,51479,51510
%N Numbers that are the sum of seven fifth powers in exactly two ways.
%C Differs from A345605 at term 156 because 84457 = 2^5 + 4^5 + 4^5 + 6^5 + 6^5 + 6^5 + 9^5 = 1^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 8^5 = 1^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 8^5.
%H Sean A. Irvine, <a href="/A346279/b346279.txt">Table of n, a(n) for n = 1..10000</a>
%e 4099 is a term because 4099 = 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.
%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, 7):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 2])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A345605, A345824, A346278, A346280, A346327, A346357.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jul 13 2021
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