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A346326 Numbers that are the sum of eight fifth powers in exactly one way. 6

%I #7 Jul 31 2021 19:03:38

%S 8,39,70,101,132,163,194,225,250,256,281,312,343,374,405,436,467,492,

%T 523,554,585,616,647,678,734,765,796,827,858,889,976,1007,1031,1038,

%U 1062,1069,1093,1100,1124,1155,1186,1217,1218,1248,1249,1273,1280,1304,1311

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

%C Differs from A003353 at term 156 because 4100 = 1^5 + 1^5 + 1^5 + 3^5 + 3^5 + 3^5 + 3^5 + 5^5 = 1^5 + 1^5 + 1^5 + 1^5 + 4^5 + 4^5 + 4^5 + 4^5.

%H Sean A. Irvine, <a href="/A346326/b346326.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 is a term because 8 = 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, 8):

%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. A003353, A345833, A346278, A346327, A346336.

%K nonn

%O 1,1

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

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