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 A345853 Numbers that are the sum of ten fourth powers in exactly one ways. 6

%I #6 Jul 31 2021 20:00:03

%S 10,25,40,55,70,85,90,100,105,115,120,130,135,145,150,160,165,170,180,

%T 185,195,200,210,215,225,230,245,250,260,275,290,330,370,385,400,410,

%U 435,450,465,490,500,515,530,570,610,625,634,640,649,650,664,675,679

%N Numbers that are the sum of ten fourth powers in exactly one ways.

%C Differs from A003344 at term 30 because 265 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4.

%H Sean A. Irvine, <a href="/A345853/b345853.txt">Table of n, a(n) for n = 1..10000</a>

%e 25 is a term because 25 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4.

%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**4 for x in range(1, 1000)]

%o for pos in cwr(power_terms, 10):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v == 1])

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

%o print(rets[x])

%Y Cf. A003344, A345803, A345843, A345854, A346346.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, Jun 26 2021

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