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A344365 Numbers that are the sum of three fourth powers in exactly five ways.

%I A344365 #6 Jul 31 2021 22:17:19
%S A344365 1234349298,1289202642,1948502738,2935465442,4162186322,5632212978,
%T A344365 7360969778,8657437698,8753497298,11079947522,15784025138,17536524642,
%U A344365 19749588768,20627242272,21318234098,31176043808,35240346162,37459676898,39912730578,42901649042
%N A344365 Numbers that are the sum of three fourth powers in exactly five ways.
%H A344365 Sean A. Irvine, <a href="/A344365/b344365.txt">Table of n, a(n) for n = 1..946</a>
%e A344365 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 A344365 (Python)
%o A344365 from itertools import combinations_with_replacement as cwr
%o A344365 from collections import defaultdict
%o A344365 keep = defaultdict(lambda: 0)
%o A344365 power_terms = [x**4 for x in range(1, 500)]
%o A344365 for pos in cwr(power_terms, 3):
%o A344365     tot = sum(pos)
%o A344365     keep[tot] += 1
%o A344365 rets = sorted([k for k, v in keep.items() if v == 5])
%o A344365 for x in range(len(rets)):
%o A344365     print(rets[x])
%Y A344365 Cf. A343970, A344278, A344357, A344364, A344648.
%K A344365 nonn
%O A344365 1,1
%A A344365 _Sean A. Irvine_, May 15 2021