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A346356 Numbers that are the sum of six fifth powers in exactly one way.

%I A346356 #7 Jul 31 2021 19:24:01
%S A346356 6,37,68,99,130,161,192,248,279,310,341,372,403,490,521,552,583,614,
%T A346356 732,763,794,825,974,1005,1029,1036,1060,1091,1122,1153,1184,1216,
%U A346356 1247,1271,1302,1333,1364,1395,1458,1513,1544,1575,1606,1755,1786,1817,1997,2028
%N A346356 Numbers that are the sum of six fifth powers in exactly one way.
%C A346356 Differs from A003351 at term 93 because 4098 = 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.
%H A346356 Sean A. Irvine, <a href="/A346356/b346356.txt">Table of n, a(n) for n = 1..10000</a>
%e A346356 6 is a term because 6 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
%o A346356 (Python)
%o A346356 from itertools import combinations_with_replacement as cwr
%o A346356 from collections import defaultdict
%o A346356 keep = defaultdict(lambda: 0)
%o A346356 power_terms = [x**5 for x in range(1, 1000)]
%o A346356 for pos in cwr(power_terms, 6):
%o A346356     tot = sum(pos)
%o A346356     keep[tot] += 1
%o A346356     rets = sorted([k for k, v in keep.items() if v == 1])
%o A346356     for x in range(len(rets)):
%o A346356         print(rets[x])
%Y A346356 Cf. A003351, A344643, A345813, A346278, A346357.
%K A346356 nonn
%O A346356 1,1
%A A346356 _David Consiglio, Jr._, Jul 13 2021