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A344237 Numbers that are the sum of five fourth powers in exactly two ways.

%I A344237 #8 Jul 31 2021 22:02:49
%S A344237 260,275,340,515,884,1555,2595,2660,2675,2690,2705,2755,2770,2835,
%T A344237 2930,2945,3010,3185,3299,3314,3379,3554,3923,3970,3985,4050,4115,
%U A344237 4145,4160,4210,4290,4355,4400,4465,4594,4769,4834,5075,5090,5155,5265,5330,5395,5440,5505,5570,5699,6370,6545,6580,6595,6660,6675
%N A344237 Numbers that are the sum of five fourth powers in exactly two ways.
%C A344237 Differs from A344237 at term 31 because 4225 = 2^4 + 2^4 + 2^4 + 3^4 + 8^4 = 2^4 + 4^4 + 4^4 + 6^4 + 7^4 = 3^4 + 4^4 + 6^4 + 6^4 + 6^4
%H A344237 David Consiglio, Jr., <a href="/A344237/b344237.txt">Table of n, a(n) for n = 1..20000</a>
%e A344237 340 is a member of this sequence because 340 = 1^4 + 1^4 + 1^4 + 3^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4
%o A344237 (Python)
%o A344237 from itertools import combinations_with_replacement as cwr
%o A344237 from collections import defaultdict
%o A344237 keep = defaultdict(lambda: 0)
%o A344237 power_terms = [x**4 for x in range(1,50)]
%o A344237 for pos in cwr(power_terms,5):
%o A344237     tot = sum(pos)
%o A344237     keep[tot] += 1
%o A344237 rets = sorted([k for k,v in keep.items() if v == 2])
%o A344237 for x in range(len(rets)):
%o A344237     print(rets[x])
%Y A344237 Cf. A048927, A342686, A344190, A344193, A344238, A344244, A345814.
%K A344237 nonn
%O A344237 1,1
%A A344237 _David Consiglio, Jr._, May 12 2021