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A346334 Numbers that are the sum of eight fifth powers in exactly nine ways.

%I A346334 #6 Jul 31 2021 19:04:08
%S A346334 8742208,18913169,19987308,20135313,21505583,21512966,21563089,
%T A346334 21727552,22237510,22256608,22438990,22545600,22686818,23106589,
%U A346334 23122550,23189782,23221517,23287858,23346048,23477344,23798742,23847285,23931325,24138358,24385108,24394139
%N A346334 Numbers that are the sum of eight fifth powers in exactly nine ways.
%C A346334 Differs from A345617 at term 2 because 15539667 = 1^5 + 7^5 + 8^5 + 8^5 + 8^5 + 14^5 + 14^5 + 27^5 = 1^5 + 4^5 + 7^5 + 9^5 + 13^5 + 13^5 + 13^5 + 27^5 = 1^5 + 1^5 + 7^5 + 7^5 + 10^5 + 16^5 + 19^5 + 26^5 = 1^5 + 1^5 + 2^5 + 10^5 + 12^5 + 17^5 + 18^5 + 26^5 = 2^5 + 2^5 + 3^5 + 8^5 + 9^5 + 16^5 + 23^5 + 24^5 = 4^5 + 11^5 + 13^5 + 13^5 + 15^5 + 15^5 + 22^5 + 24^5 = 5^5 + 6^5 + 13^5 + 15^5 + 15^5 + 19^5 + 20^5 + 24^5 = 3^5 + 10^5 + 12^5 + 12^5 + 18^5 + 18^5 + 20^5 + 24^5 = 6^5 + 9^5 + 11^5 + 11^5 + 15^5 + 21^5 + 22^5 + 22^5 = 3^5 + 5^5 + 10^5 + 19^5 + 19^5 + 20^5 + 20^5 + 21^5.
%H A346334 Sean A. Irvine, <a href="/A346334/b346334.txt">Table of n, a(n) for n = 1..10000</a>
%e A346334 8742208 is a term because 8742208 = 1^5 + 1^5 + 2^5 + 3^5 + 5^5 + 7^5 + 15^5 + 24^5 = 4^5 + 4^5 + 8^5 + 8^5 + 9^5 + 15^5 + 17^5 + 23^5 = 1^5 + 3^5 + 7^5 + 12^5 + 12^5 + 13^5 + 17^5 + 23^5 = 2^5 + 5^5 + 6^5 + 7^5 + 15^5 + 15^5 + 15^5 + 23^5 = 1^5 + 1^5 + 9^5 + 9^5 + 11^5 + 17^5 + 18^5 + 22^5 = 3^5 + 3^5 + 7^5 + 9^5 + 12^5 + 12^5 + 21^5 + 21^5 = 4^5 + 4^5 + 4^5 + 11^5 + 11^5 + 12^5 + 21^5 + 21^5 = 10^5 + 12^5 + 12^5 + 13^5 + 16^5 + 16^5 + 19^5 + 20^5 = 8^5 + 13^5 + 14^5 + 14^5 + 14^5 + 16^5 + 19^5 + 20^5.
%o A346334 (Python)
%o A346334 from itertools import combinations_with_replacement as cwr
%o A346334 from collections import defaultdict
%o A346334 keep = defaultdict(lambda: 0)
%o A346334 power_terms = [x**5 for x in range(1, 1000)]
%o A346334 for pos in cwr(power_terms, 8):
%o A346334     tot = sum(pos)
%o A346334     keep[tot] += 1
%o A346334     rets = sorted([k for k, v in keep.items() if v == 9])
%o A346334     for x in range(len(rets)):
%o A346334         print(rets[x])
%Y A346334 Cf. A345617, A345841, A346286, A346333, A346335, A346344.
%K A346334 nonn
%O A346334 1,1
%A A346334 _David Consiglio, Jr._, Jul 13 2021