%I #12 May 10 2024 02:20:28

%S 260,275,340,515,884,1555,2595,2660,2675,2690,2705,2755,2770,2835,

%T 2930,2945,3010,3185,3299,3314,3379,3554,3923,3970,3985,4050,4115,

%U 4145,4160,4210,4225,4290,4355,4400,4465,4594,4769,4834,5075,5090,5155,5265,5330,5395,5440,5505,5570,5699,6370,6545,6580,6595,6610

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

%H David Consiglio, Jr., <a href="/A344238/b344238.txt">Table of n, a(n) for n = 1..20000</a>

%e 340 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4

%e = 2^4 + 3^4 + 3^4 + 3^4 + 3^4

%e so 340 is a term of this sequence.

%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, 50)]

%o for pos in cwr(power_terms, 5):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k, v in keep.items() if v >= 2])

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

%o print(rets[x])

%Y Cf. A003339, A309763, A342685, A343702, A344237, A344243, A345559.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 12 2021