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A344192 Numbers that are the sum of three fourth powers in exactly two ways.

%I A344192 #10 Jul 31 2021 22:17:10
%S A344192 2673,6578,16562,28593,35378,42768,43218,54977,94178,105248,106353,
%T A344192 122018,134162,137633,149058,171138,177042,178737,181202,195122,
%U A344192 195858,198497,216513,234273,235298,235553,264113,264992,300833,318402,318882,324818,334802,346673,364658,384833,439922,457488
%N A344192 Numbers that are the sum of three fourth powers in exactly two ways.
%C A344192 Differs from A309762 at term 59 because 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4
%H A344192 David Consiglio, Jr., <a href="/A344192/b344192.txt">Table of n, a(n) for n = 1..10000</a>
%e A344192 16562 is a member of this sequence because 16562 = 1^4 + 9^4 + 10^4 = 5^4 + 6^4 + 11^4
%o A344192 (Python)
%o A344192 from itertools import combinations_with_replacement as cwr
%o A344192 from collections import defaultdict
%o A344192 keep = defaultdict(lambda: 0)
%o A344192 power_terms = [x**4 for x in range(1,50)]
%o A344192 for pos in cwr(power_terms,3):
%o A344192     tot = sum(pos)
%o A344192     keep[tot] += 1
%o A344192 rets = sorted([k for k,v in keep.items() if v == 2])
%o A344192 for x in range(len(rets)):
%o A344192     print(rets[x])
%Y A344192 Cf. A025396, A309762, A344188, A344193, A344240.
%K A344192 nonn
%O A344192 1,1
%A A344192 _David Consiglio, Jr._, May 11 2021