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A344188 Numbers that are the sum of three fourth powers in exactly one way.

%I A344188 #14 Jul 23 2025 16:02:52
%S A344188 3,18,33,48,83,98,113,163,178,243,258,273,288,338,353,418,513,528,593,
%T A344188 627,642,657,707,722,768,787,882,897,962,1137,1251,1266,1298,1313,
%U A344188 1328,1331,1378,1393,1458,1506,1553,1568,1633,1808,1875,1922,1937,2002,2177,2403,2418,2433,2483,2498,2546,2563,2593,2608,2658
%N A344188 Numbers that are the sum of three fourth powers in exactly one way.
%C A344188 Differs from A003337 and A047714 at term 60 because 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4, see A309762.
%H A344188 David Consiglio, Jr., <a href="/A344188/b344188.txt">Table of n, a(n) for n = 1..20000</a>
%e A344188 33 is a member of this sequence because 33 = 1^4 + 2^4 + 2^4
%o A344188 (Python)
%o A344188 from itertools import combinations_with_replacement as cwr
%o A344188 from collections import defaultdict
%o A344188 keep = defaultdict(lambda: 0)
%o A344188 power_terms = [x**4 for x in range(1,50)]
%o A344188 for pos in cwr(power_terms,3):
%o A344188     tot = sum(pos)
%o A344188     keep[tot] += 1
%o A344188 rets = sorted([k for k,v in keep.items() if v == 1])
%o A344188 for x in range(len(rets)):
%o A344188     print(rets[x])
%Y A344188 Cf. A003337, A025395, A344187, A344189, A344192, A344641.
%K A344188 nonn
%O A344188 1,1
%A A344188 _David Consiglio, Jr._, May 11 2021