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A345609 Numbers that are the sum of seven fifth powers in six or more ways. 7

%I #8 Jul 31 2021 16:25:22

%S 13562501,14583968,21555313,22057487,22066065,23089782,23345024,

%T 24217918,24401574,24855016,24952718,24993517,25052501,25385064,

%U 28608832,29558618,30653536,31613713,32559143,33005785,33533765,33635825,33828631,34267551,34268332,35431351

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

%H Sean A. Irvine, <a href="/A345609/b345609.txt">Table of n, a(n) for n = 1..10000</a>

%e 14583968 is a term because 14583968 = 1^5 + 4^5 + 14^5 + 16^5 + 19^5 + 21^5 + 23^5 = 2^5 + 4^5 + 14^5 + 14^5 + 20^5 + 22^5 + 22^5 = 4^5 + 5^5 + 10^5 + 15^5 + 20^5 + 21^5 + 23^5 = 6^5 + 8^5 + 9^5 + 15^5 + 15^5 + 20^5 + 25^5 = 6^5 + 8^5 + 14^5 + 14^5 + 14^5 + 16^5 + 26^5 = 6^5 + 10^5 + 12^5 + 12^5 + 16^5 + 16^5 + 26^5.

%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 >= 6])

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

%o print(rets[x])

%Y Cf. A345572, A345608, A345614, A345629, A345720, A346283.

%K nonn

%O 1,1

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

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Last modified June 22 15:06 EDT 2024. Contains 373587 sequences. (Running on oeis4.)