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A346329 Numbers that are the sum of eight fifth powers in exactly four ways.

%I A346329 #7 Jul 31 2021 19:03:48
%S A346329 391250,392031,455750,519236,604822,622281,672023,672054,672265,
%T A346329 673554,697492,703978,707368,730259,763292,857761,893605,893636,
%U A346329 893816,893847,894027,894058,894452,894628,896729,897151,901380,903839,909124,909597,910411,911403
%N A346329 Numbers that are the sum of eight fifth powers in exactly four ways.
%C A346329 Differs from A345612 at term 33 because 926372 = 5^5 + 6^5 + 6^5 + 6^5 + 6^5 + 8^5 + 10^5 + 15^5 = 4^5 + 6^5 + 6^5 + 7^5 + 7^5 + 7^5 + 10^5 + 15^5 = 2^5 + 5^5 + 8^5 + 8^5 + 8^5 + 8^5 + 8^5 + 15^5 = 2^5 + 2^5 + 7^5 + 7^5 + 8^5 + 11^5 + 11^5 + 14^5 = 2^5 + 2^5 + 6^5 + 7^5 + 8^5 + 12^5 + 12^5 + 13^5.
%H A346329 Sean A. Irvine, <a href="/A346329/b346329.txt">Table of n, a(n) for n = 1..10000</a>
%e A346329 391250 is a term because 391250 = 2^5 + 3^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 1^5 + 1^5 + 4^5 + 7^5 + 8^5 + 8^5 + 9^5 + 12^5 = 2^5 + 3^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 3^5 + 3^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5.
%o A346329 (Python)
%o A346329 from itertools import combinations_with_replacement as cwr
%o A346329 from collections import defaultdict
%o A346329 keep = defaultdict(lambda: 0)
%o A346329 power_terms = [x**5 for x in range(1, 1000)]
%o A346329 for pos in cwr(power_terms, 8):
%o A346329     tot = sum(pos)
%o A346329     keep[tot] += 1
%o A346329     rets = sorted([k for k, v in keep.items() if v == 4])
%o A346329     for x in range(len(rets)):
%o A346329         print(rets[x])
%Y A346329 Cf. A345612, A345836, A346281, A346328, A346330, A346339.
%K A346329 nonn
%O A346329 1,1
%A A346329 _David Consiglio, Jr._, Jul 13 2021