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A345608 Numbers that are the sum of seven fifth powers in five or more ways. 7

%I #6 Jul 31 2021 16:25:18

%S 6768576,6776120,7883668,8625376,8740709,10036201,10604054,12476826,

%T 12618493,13006575,13060213,13080706,13174250,13536416,13550162,

%U 13562501,13662500,14110656,14583968,15169276,15247994,16053313,16060683,16374218,16573507,16600001

%N Numbers that are the sum of seven fifth powers in five or more ways.

%H Sean A. Irvine, <a href="/A345608/b345608.txt">Table of n, a(n) for n = 1..4721</a>

%e 6776120 is a term because 6776120 = 2^5 + 4^5 + 7^5 + 12^5 + 17^5 + 18^5 + 20^5 = 3^5 + 6^5 + 6^5 + 12^5 + 14^5 + 18^5 + 21^5 = 4^5 + 6^5 + 8^5 + 11^5 + 13^5 + 16^5 + 22^5 = 4^5 + 7^5 + 7^5 + 7^5 + 16^5 + 19^5 + 20^5 = 5^5 + 6^5 + 6^5 + 8^5 + 16^5 + 19^5 + 20^5.

%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, 7):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 5])

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

%o print(rets[x])

%Y Cf. A345571, A345607, A345609, A345613, A345719, A346282.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 20 2021

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)