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 A345863 Numbers that are the sum of five fifth powers in five or more ways. 6

%I #6 Jul 31 2021 16:54:15

%S 9006349824,65799210368,67629776576,181085909632,188189635424,

%T 288203194368,295677350451,467139768468,471359089024,656243139157,

%U 691381929281,797466940832,854533526901,874953049024,891862586132,953769598750,1038549256768

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

%H Sean A. Irvine, <a href="/A345863/b345863.txt">Table of n, a(n) for n = 1..168</a>

%e 65799210368 is a term because 65799210368 = 7^5 + 77^5 + 109^5 + 115^5 + 125^5 = 10^5 + 84^5 + 98^5 + 109^5 + 132^5 = 16^5 + 21^5 + 29^5 + 71^5 + 146^5 = 49^5 + 57^5 + 77^5 + 115^5 + 135^5 = 57^5 + 59^5 + 63^5 + 125^5 + 129^5.

%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, 5):

%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, A344518, A345719, A345864, A346257.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 27 2021

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)