cp's OEIS Frontend

A345578 Numbers that are the sum of eight fourth powers in three or more ways.

%I A345578 #6 Jul 31 2021 17:51:30
%S A345578 518,2678,2693,2708,2738,2758,2773,2838,2853,2868,2883,2918,2933,2948,
%T A345578 2998,3013,3078,3108,3123,3173,3188,3253,3302,3317,3363,3382,3428,
%U A345578 3477,3492,3542,3557,3622,3732,3778,3797,3893,3926,3953,3973,3988,4018,4053,4101
%N A345578 Numbers that are the sum of eight fourth powers in three or more ways.
%H A345578 Sean A. Irvine, <a href="/A345578/b345578.txt">Table of n, a(n) for n = 1..10000</a>
%e A345578 2678 is a term because 2678 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 7^4.
%o A345578 (Python)
%o A345578 from itertools import combinations_with_replacement as cwr
%o A345578 from collections import defaultdict
%o A345578 keep = defaultdict(lambda: 0)
%o A345578 power_terms = [x**4 for x in range(1, 1000)]
%o A345578 for pos in cwr(power_terms, 8):
%o A345578     tot = sum(pos)
%o A345578     keep[tot] += 1
%o A345578     rets = sorted([k for k, v in keep.items() if v >= 3])
%o A345578     for x in range(len(rets)):
%o A345578         print(rets[x])
%Y A345578 Cf. A345533, A345569, A345577, A345579, A345587, A345611, A345835.
%K A345578 nonn
%O A345578 1,1
%A A345578 _David Consiglio, Jr._, Jun 20 2021