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A345639 Numbers that are the sum of ten fifth powers in seven or more ways.

%I A345639 #6 Jul 31 2021 15:58:45
%S A345639 555098,674040,683166,707315,763631,777852,778844,780945,783224,
%T A345639 893654,896500,897668,920887,926616,927819,928802,936850,937631,
%U A345639 944383,945017,952897,953077,953139,953350,953414,955178,963131,975133,979482,984133,985453,985664
%N A345639 Numbers that are the sum of ten fifth powers in seven or more ways.
%H A345639 Sean A. Irvine, <a href="/A345639/b345639.txt">Table of n, a(n) for n = 1..10000</a>
%e A345639 674040 is a term because 674040 = 1^5 + 1^5 + 2^5 + 3^5 + 3^5 + 7^5 + 9^5 + 10^5 + 12^5 + 12^5 = 1^5 + 1^5 + 2^5 + 4^5 + 4^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 = 1^5 + 3^5 + 3^5 + 3^5 + 5^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 = 1^5 + 3^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 = 2^5 + 2^5 + 2^5 + 2^5 + 4^5 + 6^5 + 8^5 + 10^5 + 11^5 + 13^5 = 2^5 + 3^5 + 3^5 + 4^5 + 4^5 + 6^5 + 6^5 + 9^5 + 9^5 + 14^5 = 3^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 7^5 + 8^5 + 12^5 + 13^5.
%o A345639 (Python)
%o A345639 from itertools import combinations_with_replacement as cwr
%o A345639 from collections import defaultdict
%o A345639 keep = defaultdict(lambda: 0)
%o A345639 power_terms = [x**5 for x in range(1, 1000)]
%o A345639 for pos in cwr(power_terms, 10):
%o A345639     tot = sum(pos)
%o A345639     keep[tot] += 1
%o A345639     rets = sorted([k for k, v in keep.items() if v >= 7])
%o A345639     for x in range(len(rets)):
%o A345639         print(rets[x])
%Y A345639 Cf. A345600, A345624, A345638, A345640, A346352.
%K A345639 nonn
%O A345639 1,1
%A A345639 _David Consiglio, Jr._, Jun 20 2021