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A344244 Numbers that are the sum of five fourth powers in exactly three ways.

%I A344244 #7 Jul 31 2021 22:02:52
%S A344244 4225,6610,6850,9170,9235,9490,11299,12929,14209,14690,14755,14770,
%T A344244 15314,16579,16594,16659,16834,17203,17235,17315,17859,17874,17939,
%U A344244 18785,18850,18979,19154,19700,19715,20674,21250,21330,21364,21410,21954,23139,23795,24754,25810,26578,28610,28930,29330,29699
%N A344244 Numbers that are the sum of five fourth powers in exactly three ways.
%C A344244 Differs from A344243 at term 31 because 20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4 = 2^4 + 3^4 + 3^4 + 3^4 + 12^4 = 2^4 + 6^4 + 9^4 + 9^4 + 9^4 = 4^4 + 6^4 + 7^4 + 7^4 + 11^4
%H A344244 David Consiglio, Jr., <a href="/A344244/b344244.txt">Table of n, a(n) for n = 1..20000</a>
%e A344244 6850 is a member of this sequence because 6850 =  = 1^4 + 2^4 + 2^4 + 4^4 + 9^4 = 2^4 + 3^4 + 4^4 + 7^4 + 8^4 = 3^4 + 3^4 + 6^4 + 6^4 + 8^4
%o A344244 (Python)
%o A344244 from itertools import combinations_with_replacement as cwr
%o A344244 from collections import defaultdict
%o A344244 keep = defaultdict(lambda: 0)
%o A344244 power_terms = [x**4 for x in range(1,50)]
%o A344244 for pos in cwr(power_terms,5):
%o A344244     tot = sum(pos)
%o A344244     keep[tot] += 1
%o A344244 rets = sorted([k for k,v in keep.items() if v == 3])
%o A344244 for x in range(len(rets)):
%o A344244     print(rets[x])
%Y A344244 Cf. A342688, A343705, A344237, A344242, A344243, A344355, A345815.
%K A344244 nonn
%O A344244 1,1
%A A344244 _David Consiglio, Jr._, May 12 2021