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A345562 Numbers that are the sum of six fourth powers in five or more ways. 8

%I #6 Jul 31 2021 18:05:10

%S 15395,16610,18866,19235,19410,20996,21011,21251,21316,21331,21491,

%T 21620,23811,25091,29700,29715,29906,29955,30356,30995,31235,31266,

%U 31331,31506,32035,33651,33795,33891,35171,35411,35636,35796,35971,37811,37971,38051,38595

%N Numbers that are the sum of six fourth powers in five or more ways.

%H Sean A. Irvine, <a href="/A345562/b345562.txt">Table of n, a(n) for n = 1..10000</a>

%e 16610 is a term because 16610 = 1^4 + 2^4 + 2^4 + 2^4 + 9^4 + 10^4 = 2^4 + 2^4 + 2^4 + 5^4 + 6^4 + 11^4 = 2^4 + 2^4 + 3^4 + 7^4 + 8^4 + 10^4 = 4^4 + 4^4 + 6^4 + 7^4 + 7^4 + 10^4 = 5^4 + 6^4 + 7^4 + 8^4 + 8^4 + 8^4.

%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**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 6):

%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. A344358, A345514, A345561, A345563, A345571, A345719, A345817.

%K nonn

%O 1,1

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

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Last modified June 15 10:58 EDT 2024. Contains 373407 sequences. (Running on oeis4.)