login
Numbers that are the sum of six fifth powers in five or more ways.
7

%I #6 Jul 31 2021 16:37:35

%S 54827300,74115800,74883600,75609125,113088250,120274275,166078869,

%T 169692136,174781858,178736448,182341225,185558208,194939538,

%U 203054589,218814275,235067008,250989825,251772882,252721458,255453233,258124975,274616694,282859667

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

%H Sean A. Irvine, <a href="/A345719/b345719.txt">Table of n, a(n) for n = 1..10000</a>

%e 74115800 is a term because 74115800 = 1^5 + 4^5 + 21^5 + 21^5 + 29^5 + 34^5 = 1^5 + 8^5 + 14^5 + 23^5 + 32^5 + 32^5 = 4^5 + 11^5 + 13^5 + 22^5 + 24^5 + 36^5 = 5^5 + 6^5 + 19^5 + 20^5 + 24^5 + 36^5 = 6^5 + 25^5 + 25^5 + 25^5 + 29^5 + 30^5.

%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 >= 5])

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

%o print(rets[x])

%Y Cf. A345562, A345608, A345718, A345720, A345863, A346360.

%K nonn

%O 1,1

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