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A344642 Numbers that are the sum of four fifth powers in exactly one way.

%I A344642 #6 Jul 31 2021 19:38:16
%S A344642 4,35,66,97,128,246,277,308,339,488,519,550,730,761,972,1027,1058,
%T A344642 1089,1120,1269,1300,1331,1511,1542,1753,2050,2081,2112,2292,2323,
%U A344642 2534,3073,3104,3128,3159,3190,3221,3315,3370,3401,3432,3612,3643,3854,4096,4151,4182,4213,4393,4424,4635,5174,5205,5416,6197,6252
%N A344642 Numbers that are the sum of four fifth powers in exactly one way.
%C A344642 Differs from A003349 at term 270 because 51445 = 4^5 + 8^5 + 8^5 + 8^5 = 6^5 + 7^5 + 7^5 + 9^5
%H A344642 David Consiglio, Jr., <a href="/A344642/b344642.txt">Table of n, a(n) for n = 1..20000</a>
%e A344642 66 is a term because 66 = 1^5 + 1^5 + 2^5 + 2^5
%o A344642 (Python)
%o A344642 from itertools import combinations_with_replacement as cwr
%o A344642 from collections import defaultdict
%o A344642 keep = defaultdict(lambda: 0)
%o A344642 power_terms = [x**5 for x in range(1, 500)]
%o A344642 for pos in cwr(power_terms, 4):
%o A344642     tot = sum(pos)
%o A344642     keep[tot] += 1
%o A344642 rets = sorted([k for k, v in keep.items() if v == 1])
%o A344642 for x in range(len(rets)):
%o A344642     print(rets[x])
%Y A344642 Cf. A003349, A344189, A344641, A344643, A344645.
%K A344642 nonn
%O A344642 1,1
%A A344642 _David Consiglio, Jr._, May 25 2021