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 A345721 Numbers that are the sum of six fifth powers in seven or more ways. 6

%I

%S 1184966816,1700336000,1717860100,1972000800,2229475325,2295937600,

%T 2396275200,2548597632,2625460992,2886251808,3217068800,3697267200,

%U 3729261536,3765398725,4046532448,4165116967,4246566632,4286704224,4335900525,4489548050

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

%H Sean A. Irvine, <a href="/A345721/b345721.txt">Table of n, a(n) for n = 1..4091</a>

%e 1700336000 is a term because 1700336000 = 4^5 + 17^5 + 31^5 + 37^5 + 43^5 + 68^5 = 6^5 + 9^5 + 10^5 + 23^5 + 60^5 + 62^5 = 6^5 + 14^5 + 16^5 + 50^5 + 50^5 + 64^5 = 7^5 + 25^5 + 30^5 + 54^5 + 56^5 + 58^5 = 8^5 + 21^5 + 23^5 + 27^5 + 57^5 + 64^5 = 9^5 + 21^5 + 22^5 + 29^5 + 53^5 + 66^5 = 13^5 + 32^5 + 35^5 + 38^5 + 45^5 + 67^5.

%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, 6):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 7])

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

%o print(rets[x])

%Y Cf. A345564, A345629, A345720, A345722, A346362.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 24 2021

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Last modified January 25 19:00 EST 2022. Contains 350572 sequences. (Running on oeis4.)