A345589 - OEIS

%I #6 Jul 31 2021 17:38:55

%S 3189,4149,4229,4244,4309,4374,4404,4419,4469,4484,4549,4659,4724,

%T 4853,4899,5028,5093,5139,5189,5204,5269,5284,5349,5379,5414,5444,

%U 5459,5509,5524,5574,5589,5619,5634,5654,5684,5699,5749,5764,5814,5829,5939,6068,6133

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

%H Sean A. Irvine, <a href="/A345589/b345589.txt">Table of n, a(n) for n = 1..10000</a>

%e 4149 is a term because 4149 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 8^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 6^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 6^4 + 7^4 = 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 + 6^4 = 4^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4.

%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, 9):

%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. A345544, A345580, A345588, A345590, A345598, A345622, A345847.

%K nonn

%O 1,1

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