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A344242 Numbers that are the sum of four fourth powers in exactly three ways.

%I A344242 #8 Jul 31 2021 22:12:02
%S A344242 16578,43234,49329,53218,54978,57154,93393,106354,107649,108754,
%T A344242 138258,151219,160434,168963,173539,177699,178738,181138,183603,
%U A344242 185298,195378,195859,196418,197154,197778,201683,202419,209763,211249,216594,217138,223074,234274,235554,235569,237249,237699,240834
%N A344242 Numbers that are the sum of four fourth powers in exactly three ways.
%C A344242 Differs from A344241 at term 36 because 236674 = 1^4 + 2^4 + 7^4 + 22^4 = 3^4 + 6^4 + 18^4 + 19^4 = 7^4 + 14^4 + 16^4 + 19^4 = 8^4 + 16^4 + 17^4 + 17^4
%H A344242 David Consiglio, Jr., <a href="/A344242/b344242.txt">Table of n, a(n) for n = 1..20000</a>
%e A344242 49329 is a member of this sequence because 49329 = 2^4 + 2^4 + 12^4 + 13^4 = 4^4 + 8^4 + 9^4 + 14^4 = 6^4 + 9^4 + 12^4 + 12^4
%o A344242 (Python)
%o A344242 from itertools import combinations_with_replacement as cwr
%o A344242 from collections import defaultdict
%o A344242 keep = defaultdict(lambda: 0)
%o A344242 power_terms = [x**4 for x in range(1,50)]
%o A344242 for pos in cwr(power_terms,4):
%o A344242     tot = sum(pos)
%o A344242     keep[tot] += 1
%o A344242 rets = sorted([k for k,v in keep.items() if v == 3])
%o A344242 for x in range(len(rets)):
%o A344242     print(rets[x])
%Y A344242 Cf. A025405, A344193, A344240, A344241, A344244, A344353.
%K A344242 nonn
%O A344242 1,1
%A A344242 _David Consiglio, Jr._, May 12 2021