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A346327 Numbers that are the sum of eight fifth powers in exactly two ways. 7

%I

%S 4100,4131,4162,4193,4342,4373,4404,4584,4615,4826,5123,5154,5185,

%T 5365,5396,5607,6146,6177,6388,7169,7224,7255,7286,7466,7497,7708,

%U 8247,8278,8489,9270,10348,10379,10590,11371,11875,11906,11937,12117,12148,12359,12898

%N Numbers that are the sum of eight fifth powers in exactly two ways.

%C Differs from A345610 at term 128 because 52417 = 3^5 + 3^5 + 3^5 + 3^5 + 5^5 + 6^5 + 6^5 + 8^5 = 1^5 + 4^5 + 4^5 + 4^5 + 4^5 + 6^5 + 6^5 + 8^5 = 3^5 + 3^5 + 3^5 + 3^5 + 4^5 + 7^5 + 7^5 + 7^5.

%H Sean A. Irvine, <a href="/A346327/b346327.txt">Table of n, a(n) for n = 1..10000</a>

%e 4100 is a term 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.

%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 == 2])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A345610, A345834, A346279, A346326, A346328, A346337.

%K nonn

%O 1,1

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

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Last modified October 6 19:00 EDT 2022. Contains 357270 sequences. (Running on oeis4.)