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A345605 Numbers that are the sum of seven fifth powers in two or more ways.

%I A345605 #6 Jul 31 2021 16:25:05
%S A345605 4099,4130,4161,4341,4372,4583,5122,5153,5364,6145,7223,7254,7465,
%T A345605 8246,10347,11874,11905,12116,12897,14998,19649,20905,20936,21147,
%U A345605 21928,24029,28680,36866,36897,37108,37711,37889,39990,40138,44641,51393,51448,51479,51510
%N A345605 Numbers that are the sum of seven fifth powers in two or more ways.
%H A345605 Sean A. Irvine, <a href="/A345605/b345605.txt">Table of n, a(n) for n = 1..10000</a>
%e A345605 4130 is a term because 4130 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 4^5 = 1^5 + 2^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%o A345605 (Python)
%o A345605 from itertools import combinations_with_replacement as cwr
%o A345605 from collections import defaultdict
%o A345605 keep = defaultdict(lambda: 0)
%o A345605 power_terms = [x**5 for x in range(1, 1000)]
%o A345605 for pos in cwr(power_terms, 7):
%o A345605     tot = sum(pos)
%o A345605     keep[tot] += 1
%o A345605     rets = sorted([k for k, v in keep.items() if v >= 2])
%o A345605     for x in range(len(rets)):
%o A345605         print(rets[x])
%Y A345605 Cf. A003352, A345507, A345568, A345606, A345610, A346279.
%K A345605 nonn
%O A345605 1,1
%A A345605 _David Consiglio, Jr._, Jun 20 2021