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A088687 Numbers that can be represented as j^4 + k^4, with 0 < j < k, in exactly one way.

%I A088687 #19 Feb 15 2023 18:48:33
%S A088687 17,82,97,257,272,337,626,641,706,881,1297,1312,1377,1552,1921,2402,
%T A088687 2417,2482,2657,3026,3697,4097,4112,4177,4352,4721,5392,6497,6562,
%U A088687 6577,6642,6817,7186,7857,8962,10001,10016,10081,10256,10625,10657,11296
%N A088687 Numbers that can be represented as j^4 + k^4, with 0 < j < k, in exactly one way.
%H A088687 Robert Israel, <a href="/A088687/b088687.txt">Table of n, a(n) for n = 1..4500</a>
%e A088687 17 = 1^4 + 2^4.
%e A088687 635318657 = 133^4 + 134^4 is absent because it is also 59^4 + 158^4 (see A046881, A230562)
%p A088687 N:= 2*10^4: # for terms <= N
%p A088687 V:= Vector(N):
%p A088687 for j from 1 while 2*j^4 < N do
%p A088687   for k from j+1 do
%p A088687     r:= j^4 + k^4;
%p A088687     if r > N then break fi;
%p A088687     V[r]:= V[r]+1;
%p A088687 od od:
%p A088687 select(t -> V[t] = 1, [$1..N]); $ _Robert Israel_, Dec 15 2019
%t A088687 lst={};Do[Do[x=a^4;Do[y=b^4;If[x+y==n,AppendTo[lst,n]],{b,Floor[(n-x)^(1/4)],a+1,-1}],{a,Floor[n^(1/4)],1,-1}],{n,4*7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2009 *)
%o A088687 (PARI) powers2(m1,m2,p1) = { for(k=m1,m2, a=powers(k,p1); if(a==1,print1(k",")) ); } powers(n,p) = { z1=0; z2=0; c=0; cr = floor(n^(1/p)+1); for(x=1,cr, for(y=x+1,cr, z1=x^p+y^p; if(z1 == n,c++); ); ); return(c) }
%Y A088687 Cf. A003336, A088728.
%K A088687 nonn
%O A088687 1,1
%A A088687 _Cino Hilliard_, Nov 22 2003
%E A088687 Edited by _Don Reble_, May 03 2006