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A346339 Numbers that are the sum of nine fifth powers in exactly four ways.

%I A346339 #6 Jul 31 2021 19:00:54
%S A346339 55542,120350,143507,167241,182549,192233,202890,326685,327986,328247,
%T A346339 329028,329809,333257,351722,358474,358968,359210,359538,359813,
%U A346339 365404,367071,367313,374034,374846,375627,376619,377158,379259,381157,383910,384765,390396
%N A346339 Numbers that are the sum of nine fifth powers in exactly four ways.
%C A346339 Differs from A345621 at term 37 because 392063 = 2^5 + 2^5 + 4^5 + 5^5 + 5^5 + 5^5 + 8^5 + 10^5 + 12^5 = 2^5 + 2^5 + 3^5 + 3^5 + 6^5 + 7^5 + 9^5 + 9^5 + 12^5 = 2^5 + 2^5 + 4^5 + 4^5 + 4^5 + 6^5 + 9^5 + 11^5 + 11^5 = 1^5 + 2^5 + 3^5 + 4^5 + 5^5 + 8^5 + 8^5 + 11^5 + 11^5 = 1^5 + 1^5 + 1^5 + 3^5 + 8^5 + 9^5 + 10^5 + 10^5 + 10^5.
%H A346339 Sean A. Irvine, <a href="/A346339/b346339.txt">Table of n, a(n) for n = 1..10000</a>
%e A346339 55542 is a term because 55542 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 5^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 5^5 + 7^5 + 7^5 + 7^5 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 4^5 + 7^5 + 7^5 + 7^5.
%o A346339 (Python)
%o A346339 from itertools import combinations_with_replacement as cwr
%o A346339 from collections import defaultdict
%o A346339 keep = defaultdict(lambda: 0)
%o A346339 power_terms = [x**5 for x in range(1, 1000)]
%o A346339 for pos in cwr(power_terms, 9):
%o A346339     tot = sum(pos)
%o A346339     keep[tot] += 1
%o A346339     rets = sorted([k for k, v in keep.items() if v == 4])
%o A346339     for x in range(len(rets)):
%o A346339         print(rets[x])
%Y A346339 Cf. A345621, A345846, A346329, A346338, A346340, A346349.
%K A346339 nonn
%O A346339 1,1
%A A346339 _David Consiglio, Jr._, Jul 13 2021