%I #10 Jul 31 2021 22:11:55

%S 4,19,34,49,64,84,99,114,129,164,179,194,244,274,289,304,324,339,354,

%T 369,419,434,499,514,529,544,594,609,628,643,658,673,674,708,723,738,

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

%C 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 David Consiglio, Jr., <a href="/A344189/b344189.txt">Table of n, a(n) for n = 1..20000</a>

%e 34 is a member of this sequence because 34 = 1^4 + 1^4 + 2^4 + 2^4

%o (Python)

%o from itertools import combinations_with_replacement as cwr

%o from collections import defaultdict

%o keep = defaultdict(lambda: 0)

%o power_terms = [x**4 for x in range(1,50)]

%o for pos in cwr(power_terms,4):

%o tot = sum(pos)

%o keep[tot] += 1

%o rets = sorted([k for k,v in keep.items() if v == 1])

%o for x in range(len(rets)):

%o print(rets[x])

%Y Cf. A003338, A025403, A344188, A344190, A344193, A344642.

%K nonn

%O 1,1

%A _David Consiglio, Jr._, May 11 2021