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Numbers that are the sum of five positive fifth powers in four or more ways.
7

%I #12 Jan 11 2025 04:13:57

%S 287618651,1386406515,1763135232,2494769760,2619898293,3096064443,

%T 3291315732,3749564512,4045994624,5142310350,5183605813,5658934676,

%U 5880926107,7205217018,7401155424,7691215599,8429499101,8926086432,9006349824,9051501568,9203796832

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

%H Sean A. Irvine, <a href="/A344518/b344518.txt">Table of n, a(n) for n = 1..4906</a>

%e 287618651 is a term because

%e 287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5

%e = 9^5 + 13^5 + 26^5 + 37^5 + 46^5

%e = 11^5 + 12^5 + 23^5 + 41^5 + 44^5

%e = 11^5 + 20^5 + 22^5 + 30^5 + 48^5.

%e [Corrected by _Patrick De Geest_, Dec 28 2024]

%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, 500)]

%o for pos in cwr(power_terms, 5):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 4])

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

%o print(rets[x])

%Y Cf. A342685, A342686, A342687, A342688, A342687, A344519, A345718, A345863, A345864, A346257.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 21 2021