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A344193 Numbers that are the sum of four fourth powers in exactly two ways.

%I A344193 #11 Jul 23 2025 16:02:58
%S A344193 259,2674,2689,2754,2929,3298,3969,4144,4209,5074,6579,6594,6659,6769,
%T A344193 6834,7203,7874,8194,8979,9154,9234,10113,10674,11298,12673,12913,
%U A344193 13139,14674,14689,14754,16563,16643,16818,17187,17234,17299,17314,17858,18963,19699,20658,20739,20979,21154,21219,21329,21363
%N A344193 Numbers that are the sum of four fourth powers in exactly two ways.
%C A344193 Differs from A309763 at term 32 because 16578 = 1^4 + 2^4 + 9^4 + 10^4 = 2^4 + 5^4 + 6^4 + 11^4 = 3^4 + 7^4 + 8^4 + 10^4
%H A344193 David Consiglio, Jr., <a href="/A344193/b344193.txt">Table of n, a(n) for n = 1..20000</a>
%e A344193 2689 is a member of this sequence because 2689 = 2^4 + 2^4 + 4^4 + 7^4 = 2^4 + 3^4 + 6^4 + 6^4
%o A344193 (Python)
%o A344193 from itertools import combinations_with_replacement as cwr
%o A344193 from collections import defaultdict
%o A344193 keep = defaultdict(lambda: 0)
%o A344193 power_terms = [x**4 for x in range(1,50)]
%o A344193 for pos in cwr(power_terms,4):
%o A344193     tot = sum(pos)
%o A344193     keep[tot] += 1
%o A344193 rets = sorted([k for k,v in keep.items() if v == 2])
%o A344193 for x in range(len(rets)):
%o A344193     print(rets[x])
%Y A344193 Cf. A025404, A309763, A344189, A344192, A344237, A344242, A344645.
%K A344193 nonn
%O A344193 1,1
%A A344193 _David Consiglio, Jr._, May 11 2021