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%I #6 Jul 31 2021 18:53:47
%S 10,41,72,103,134,165,196,227,252,258,283,289,314,320,345,376,407,438,
%T 469,494,500,525,531,556,587,618,649,680,711,736,742,767,798,829,860,
%U 891,922,953,978,1009,1033,1040,1064,1071,1095,1102,1126,1133,1157,1164
%N Numbers that are the sum of ten fifth powers in exactly one way.
%C Differs from A003355 at term 229 because 4102 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.
%H Sean A. Irvine, <a href="/A346346/b346346.txt">Table of n, a(n) for n = 1..10000</a>
%e 10 is a term because 10 = 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5 + 1^5.
%o (Python)
%o from itertools import combinations_with_replacement as cwr
%o from collections import defaultdict
%o keep = defaultdict(lambda: 0)
%o power_terms = [x**5 for x in range(1, 1000)]
%o for pos in cwr(power_terms, 10):
%o tot = sum(pos)
%o keep[tot] += 1
%o rets = sorted([k for k, v in keep.items() if v == 1])
%o for x in range(len(rets)):
%o print(rets[x])
%Y Cf. A003355, A345853, A346336, A346347.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, Jul 13 2021
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