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A345625 Numbers that are the sum of nine fifth powers in eight or more ways.

%I A345625 #6 Jul 31 2021 16:09:22
%S A345625 1431398,1431640,1531397,1952415,1969221,2247917,2530399,2596936,
%T A345625 2652563,2652860,2736790,2851254,2965588,3088909,3148674,3273590,
%U A345625 3297416,3329120,3329362,3332244,3336895,3345442,3345653,3353186,3361614,3362217,3364738,3378178,3553641
%N A345625 Numbers that are the sum of nine fifth powers in eight or more ways.
%H A345625 Sean A. Irvine, <a href="/A345625/b345625.txt">Table of n, a(n) for n = 1..10000</a>
%e A345625 1431640 is a term because 1431640 = 1^5 + 2^5 + 3^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 = 1^5 + 2^5 + 3^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 3^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 1^5 + 4^5 + 6^5 + 7^5 + 7^5 + 8^5 + 9^5 + 12^5 + 16^5 = 2^5 + 2^5 + 3^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 2^5 + 4^5 + 4^5 + 6^5 + 8^5 + 8^5 + 9^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 3^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5.
%o A345625 (Python)
%o A345625 from itertools import combinations_with_replacement as cwr
%o A345625 from collections import defaultdict
%o A345625 keep = defaultdict(lambda: 0)
%o A345625 power_terms = [x**5 for x in range(1, 1000)]
%o A345625 for pos in cwr(power_terms, 9):
%o A345625     tot = sum(pos)
%o A345625     keep[tot] += 1
%o A345625     rets = sorted([k for k, v in keep.items() if v >= 8])
%o A345625     for x in range(len(rets)):
%o A345625         print(rets[x])
%Y A345625 Cf. A345592, A345616, A345624, A345626, A345640, A346343.
%K A345625 nonn
%O A345625 1,1
%A A345625 _David Consiglio, Jr._, Jun 20 2021