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A344187 Numbers that are the sum of two positive fourth powers in exactly one way.

%I A344187 #13 Jul 31 2021 22:21:36
%S A344187 2,17,32,82,97,162,257,272,337,512,626,641,706,881,1250,1297,1312,
%T A344187 1377,1552,1921,2402,2417,2482,2592,2657,3026,3697,4097,4112,4177,
%U A344187 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 A344187 Numbers that are the sum of two positive fourth powers in exactly one way.
%C A344187 Differs from A003336 at term 11660 because 635318657 = 59^4 + 158^4 = 133^4 + 134^4
%H A344187 David Consiglio, Jr., <a href="/A344187/b344187.txt">Table of n, a(n) for n = 1..20000</a>
%e A344187 32 is a member of this sequence because 32 = 2^4 + 2^4
%o A344187 (Python)
%o A344187 from itertools import combinations_with_replacement as cwr
%o A344187 from collections import defaultdict
%o A344187 keep = defaultdict(lambda: 0)
%o A344187 power_terms = [x**4 for x in range(1,50)]
%o A344187 for pos in cwr(power_terms,2):
%o A344187     tot = sum(pos)
%o A344187     keep[tot] += 1
%o A344187 rets = sorted([k for k,v in keep.items() if v == 1])
%o A344187 for x in range(len(rets)):
%o A344187     print(rets[x])
%Y A344187 Cf. A003336, A338667, A344188.
%K A344187 nonn
%O A344187 1,1
%A A344187 _David Consiglio, Jr._, May 11 2021