%I #6 Jul 31 2021 17:38:50

%S 2854,2919,2934,2949,2964,3014,3029,3094,3159,3174,3189,3204,3254,

%T 3269,3429,3444,3558,3573,3638,3798,3813,3974,4034,4134,4149,4164,

%U 4179,4182,4209,4214,4229,4244,4274,4294,4309,4374,4389,4404,4419,4439,4454,4469,4484

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

%H Sean A. Irvine, <a href="/A345588/b345588.txt">Table of n, a(n) for n = 1..10000</a>

%e 2919 is a term because 2919 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.

%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 >= 4])

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

%o print(rets[x])

%Y Cf. A345543, A345579, A345587, A345589, A345597, A345621, A345846.

%K nonn

%O 1,1

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