A344187 - OEIS

%I #13 Jul 31 2021 22:21:36

%S 2,17,32,82,97,162,257,272,337,512,626,641,706,881,1250,1297,1312,

%T 1377,1552,1921,2402,2417,2482,2592,2657,3026,3697,4097,4112,4177,

%U 4352,4721,4802,5392,6497,6562,6577,6642,6817,7186,7857,8192,8962,10001,10016,10081,10256,10625,10657,11296,12401,13122,14096,14642

%N Numbers that are the sum of two positive fourth powers in exactly one way.

%C Differs from A003336 at term 11660 because 635318657 = 59^4 + 158^4 = 133^4 + 134^4

%H David Consiglio, Jr., <a href="/A344187/b344187.txt">Table of n, a(n) for n = 1..20000</a>

%e 32 is a member of this sequence because 32 = 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,2):

%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. A003336, A338667, A344188.

%K nonn

%O 1,1

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