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A344643 Numbers that are the sum of five positive fifth powers in exactly one way.

%I A344643 #19 Dec 25 2024 04:10:58
%S A344643 5,36,67,98,129,160,247,278,309,340,371,489,520,551,582,731,762,793,
%T A344643 973,1004,1028,1059,1090,1121,1152,1215,1270,1301,1332,1363,1512,1543,
%U A344643 1574,1754,1785,1996,2051,2082,2113,2144,2293,2324,2355,2535,2566,2777,3074,3105,3129,3136,3160,3191,3222,3253,3316,3347,3371,3402,3433,3464,3558,3613,3644,3675,3855,3886,4128
%N A344643 Numbers that are the sum of five positive fifth powers in exactly one way.
%C A344643 Differs from A003350 at term 67 because 4097 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5.
%H A344643 David Consiglio, Jr., <a href="/A344643/b344643.txt">Table of n, a(n) for n = 1..20000</a>
%e A344643 67 is a term because 67 = 1^5 + 1^5 + 1^5 + 2^5 + 2^5.
%o A344643 (Python)
%o A344643 from itertools import combinations_with_replacement as cwr
%o A344643 from collections import defaultdict
%o A344643 keep = defaultdict(lambda: 0)
%o A344643 power_terms = [x**5 for x in range(1, 500)]
%o A344643 for pos in cwr(power_terms, 5):
%o A344643     tot = sum(pos)
%o A344643     keep[tot] += 1
%o A344643 rets = sorted([k for k, v in keep.items() if v == 1])
%o A344643 for x in range(len(rets)):
%o A344643     print(rets[x])
%Y A344643 Cf. A003350, A342686, A344190, A344642, A346356.
%K A344643 nonn
%O A344643 1,1
%A A344643 _David Consiglio, Jr._, May 25 2021
%E A344643 Name clarified by _Patrick De Geest_, Dec 24 2024