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A344241 Numbers that are the sum of four fourth powers in three or more ways.

%I A344241 #12 May 10 2024 02:20:13
%S A344241 16578,43234,49329,53218,54978,57154,93393,106354,107649,108754,
%T A344241 138258,151219,160434,168963,173539,177699,178738,181138,183603,
%U A344241 185298,195378,195859,196418,197154,197778,201683,202419,209763,211249,216594,217138,223074,234274,235554,235569,236674,237249,237699
%N A344241 Numbers that are the sum of four fourth powers in three or more ways.
%H A344241 David Consiglio, Jr., <a href="/A344241/b344241.txt">Table of n, a(n) for n = 1..20000</a>
%e A344241 49329 = 2^4 + 2^4 + 12^4 + 13^4
%e A344241       = 4^4 + 8^4 +  9^4 + 14^4
%e A344241       = 6^4 + 9^4 + 12^4 + 12^4
%e A344241 so 49329 is a term of this sequence.
%o A344241 (Python)
%o A344241 from itertools import combinations_with_replacement as cwr
%o A344241 from collections import defaultdict
%o A344241 keep = defaultdict(lambda: 0)
%o A344241 power_terms = [x**4 for x in range(1,50)]
%o A344241 for pos in cwr(power_terms,4):
%o A344241     tot = sum(pos)
%o A344241     keep[tot] += 1
%o A344241 rets = sorted([k for k,v in keep.items() if v >= 3])
%o A344241 for x in range(len(rets)):
%o A344241     print(rets[x])
%Y A344241 Cf. A025407, A309763, A344239, A344242, A344243, A344352, A345337.
%K A344241 nonn
%O A344241 1,1
%A A344241 _David Consiglio, Jr._, May 12 2021