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A344189 Numbers that are the sum of four fourth powers in exactly one way.

%I A344189 #10 Jul 31 2021 22:11:55
%S A344189 4,19,34,49,64,84,99,114,129,164,179,194,244,274,289,304,324,339,354,
%T A344189 369,419,434,499,514,529,544,594,609,628,643,658,673,674,708,723,738,
%U A344189 769,784,788,803,849,868,883,898,913,963,978,1024,1043,1138,1153,1218,1252,1267,1282,1299,1314,1329,1332,1344,1347,1379,1393
%N A344189 Numbers that are the sum of four fourth powers in exactly one way.
%C A344189 Differs from A003338 at term 14 because 259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4
%H A344189 David Consiglio, Jr., <a href="/A344189/b344189.txt">Table of n, a(n) for n = 1..20000</a>
%e A344189 34 is a member of this sequence because 34 = 1^4 + 1^4 + 2^4 + 2^4
%o A344189 (Python)
%o A344189 from itertools import combinations_with_replacement as cwr
%o A344189 from collections import defaultdict
%o A344189 keep = defaultdict(lambda: 0)
%o A344189 power_terms = [x**4 for x in range(1,50)]
%o A344189 for pos in cwr(power_terms,4):
%o A344189     tot = sum(pos)
%o A344189     keep[tot] += 1
%o A344189 rets = sorted([k for k,v in keep.items() if v == 1])
%o A344189 for x in range(len(rets)):
%o A344189     print(rets[x])
%Y A344189 Cf. A003338, A025403, A344188, A344190, A344193, A344642.
%K A344189 nonn
%O A344189 1,1
%A A344189 _David Consiglio, Jr._, May 11 2021