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A346343 Numbers that are the sum of nine fifth powers in exactly eight ways.

%I A346343 #6 Jul 31 2021 19:01:07
%S A346343 1431398,1431640,1531397,1952415,2247917,2530399,2652563,2652860,
%T A346343 2736790,2851254,2965588,3088909,3148674,3273590,3297416,3329120,
%U A346343 3329362,3332244,3336895,3345442,3345653,3361614,3362217,3364738,3553641,3571549,3577951,3609926,3610155
%N A346343 Numbers that are the sum of nine fifth powers in exactly eight ways.
%C A346343 Differs from A345625 at term 5 because 1969221 = 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 + 16^5 = 3^5 + 5^5 + 6^5 + 6^5 + 8^5 + 12^5 + 12^5 + 13^5 + 16^5 = 3^5 + 4^5 + 7^5 + 7^5 + 7^5 + 12^5 + 12^5 + 13^5 + 16^5 = 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 15^5 = 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 14^5 + 15^5 = 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 14^5 + 15^5 = 1^5 + 4^5 + 5^5 + 8^5 + 9^5 + 13^5 + 13^5 + 13^5 + 15^5 = 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 + 14^5 = 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5 + 14^5.
%H A346343 Sean A. Irvine, <a href="/A346343/b346343.txt">Table of n, a(n) for n = 1..10000</a>
%e A346343 1431398 is a term because 1431398 = 2^5 + 5^5 + 5^5 + 5^5 + 6^5 + 7^5 + 10^5 + 12^5 + 16^5 = 1^5 + 3^5 + 5^5 + 6^5 + 7^5 + 8^5 + 11^5 + 11^5 + 16^5 = 1^5 + 1^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 14^5 + 15^5 = 2^5 + 3^5 + 4^5 + 4^5 + 7^5 + 8^5 + 12^5 + 13^5 + 15^5 = 1^5 + 3^5 + 3^5 + 3^5 + 10^5 + 10^5 + 10^5 + 13^5 + 15^5 = 1^5 + 2^5 + 2^5 + 4^5 + 10^5 + 11^5 + 11^5 + 12^5 + 15^5 = 1^5 + 1^5 + 2^5 + 7^5 + 7^5 + 11^5 + 11^5 + 14^5 + 14^5 = 1^5 + 1^5 + 2^5 + 6^5 + 7^5 + 12^5 + 12^5 + 13^5 + 14^5.
%o A346343 (Python)
%o A346343 from itertools import combinations_with_replacement as cwr
%o A346343 from collections import defaultdict
%o A346343 keep = defaultdict(lambda: 0)
%o A346343 power_terms = [x**5 for x in range(1, 1000)]
%o A346343 for pos in cwr(power_terms, 9):
%o A346343     tot = sum(pos)
%o A346343     keep[tot] += 1
%o A346343     rets = sorted([k for k, v in keep.items() if v == 8])
%o A346343     for x in range(len(rets)):
%o A346343         print(rets[x])
%Y A346343 Cf. A345625, A345850, A346333, A346342, A346344, A346353.
%K A346343 nonn
%O A346343 1,1
%A A346343 _David Consiglio, Jr._, Jul 13 2021