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A344647 Numbers that are the sum of three fourth powers in six or more ways.

%I A344647 #8 Jul 31 2021 18:29:15
%S A344647 292965218,779888018,1010431058,1110995522,1500533762,1665914642,
%T A344647 2158376402,2373191618,2636686962,2689817858,3019732898,3205282178,
%U A344647 3642994082,3831800882,4324686002,4687443488,5064808658,5175310322,5745705602,6317554418,6450435362,6720346178,7018992162
%N A344647 Numbers that are the sum of three fourth powers in six or more ways.
%H A344647 Sean A. Irvine, <a href="/A344647/b344647.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..70 from David Consiglio, Jr.)
%e A344647 1010431058 is a term because 1010431058 = 13^4 + 143^4 + 156^4 = 31^4 + 132^4 + 163^4 = 44^4 + 123^4 + 167^4 = 52^4 + 117^4 + 169^4 = 69^4 + 103^4 + 172^4 = 81^4 + 92^4 + 173^4
%o A344647 (Python)
%o A344647 from itertools import combinations_with_replacement as cwr
%o A344647 from collections import defaultdict
%o A344647 keep = defaultdict(lambda: 0)
%o A344647 power_terms = [x**4 for x in range(1, 500)]
%o A344647 for pos in cwr(power_terms, 3):
%o A344647     tot = sum(pos)
%o A344647     keep[tot] += 1
%o A344647 rets = sorted([k for k, v in keep.items() if v >= 6])
%o A344647 for x in range(len(rets)):
%o A344647     print(rets[x])
%Y A344647 Cf. A344364, A344648, A344729, A344904, A345083.
%K A344647 nonn
%O A344647 1,1
%A A344647 _David Consiglio, Jr._, May 25 2021