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%I #7 Jul 31 2021 19:39:06
%S 3,34,65,96,245,276,307,487,518,729,1026,1057,1088,1268,1299,1510,
%T 2049,2080,2291,3072,3127,3158,3189,3369,3400,3611,4150,4181,4392,
%U 5173,6251,6282,6493,7274,7778,7809,7840,8020,8051,8262,8801,8832,9043,9375,9824,10902,10933,11144,11925,14026,15553,15584,15795
%N Numbers that are the sum of three fifth powers in exactly one way.
%C Differs from A003348 at term 44785 because 1375298099 = 3^5 + 55^5 + 63^5 = 25^5 + 29^5 + 68^5
%H David Consiglio, Jr., <a href="/A344641/b344641.txt">Table of n, a(n) for n = 1..20000</a>
%e 65 is a term because 65 = 1^5 + 2^5 + 2^5
%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, 500)]
%o for pos in cwr(power_terms, 3):
%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. A003348, A344188, A344642.
%K nonn
%O 1,1
%A _David Consiglio, Jr._, May 25 2021
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