%I #12 Jul 31 2021 22:17:06

%S 3,18,33,48,83,98,113,163,178,243,258,273,288,338,353,418,513,528,593,

%T 627,642,657,707,722,768,787,882,897,962,1137,1251,1266,1298,1313,

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

%C 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 David Consiglio, Jr., <a href="/A344188/b344188.txt">Table of n, a(n) for n = 1..20000</a>

%e 33 is a member of this sequence because 33 = 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,3):

%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. A003337, A025395, A344187, A344189, A344192, A344641.

%K nonn

%O 1,1

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