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Numbers that are the sum of nine fifth powers in exactly one way.
6

%I #7 Jul 31 2021 19:00:43

%S 9,40,71,102,133,164,195,226,251,257,282,288,313,344,375,406,437,468,

%T 493,499,524,555,586,617,648,679,710,735,766,797,828,859,890,921,977,

%U 1008,1032,1039,1063,1070,1094,1101,1125,1132,1156,1187,1218,1219,1249,1250

%N Numbers that are the sum of nine fifth powers in exactly one way.

%C Differs from A003354 at term 191 because 4101 = 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 + 4^5 + 4^5 + 4^5 + 4^5.

%H Sean A. Irvine, <a href="/A346336/b346336.txt">Table of n, a(n) for n = 1..10000</a>

%e 9 is a term because 9 = 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, 9):

%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. A003354, A345843, A346326, A346337, A346346.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jul 13 2021