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%I #8 Jul 31 2021 18:29:11
%S 292965218,779888018,1010431058,1110995522,1234349298,1289202642,
%T 1500533762,1665914642,1948502738,2158376402,2373191618,2636686962,
%U 2689817858,2935465442,3019732898,3205282178,3642994082,3831800882,4162186322,4324686002,4687443488,5064808658
%N Numbers that are the sum of three fourth powers in five or more ways.
%H Sean A. Irvine, <a href="/A344364/b344364.txt">Table of n, a(n) for n = 1..10000</a>
%e 292965218 is a member of this sequence because 292965218 = 2^4 + 109^4 + 111^4 = 21^4 + 98^4 + 119^4 = 27^4 + 94^4 + 121^4 = 34^4 + 89^4 + 123^4 = 49^4 + 77^4 + 126^4 = 61^4 + 66^4 + 127^4 (actually has 6 representations, so is a member of this sequence but not of A344365).
%e 1234349298 is a member of this sequence because 1234349298 = 7^4 + 154^4 + 161^4 = 26^4 + 143^4 + 169^4 = 61^4 + 118^4 + 179^4 = 74^4 + 107^4 + 181^4 = 91^4 + 91^4 + 182^4.
%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, 500)]
%o for pos in cwr(power_terms, 3):
%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. A343967, A344277, A344356, A344365, A344647.
%K nonn
%O 1,1
%A _Sean A. Irvine_, May 15 2021
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