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

17, 82, 97, 257, 272, 337, 626, 641, 706, 881, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 5392, 6497, 6562, 6577, 6642, 6817, 7186, 7857, 8962, 10001, 10016, 10081, 10256, 10625, 10657, 11296

Offset: 1

Author

Cino Hilliard, Nov 22 2003

Keywords

• nonn

Examples

			17 = 1^4 + 2^4.
635318657 = 133^4 + 134^4 is absent because it is also 59^4 + 158^4 (see A046881, A230562)
		

Links

• Robert Israel, Table of n, a(n) for n = 1..4500

Crossrefs

Cf. A003336, A088728.

Programs

Maple

N:= 2*10^4: # for terms <= N
V:= Vector(N):
for j from 1 while 2*j^4 < N do
  for k from j+1 do
    r:= j^4 + k^4;
    if r > N then break fi;
    V[r]:= V[r]+1;
od od:
select(t -> V[t] = 1, [$1..N]); $ Robert Israel, Dec 15 2019

Mathematica

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 *)

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) }

Extensions

Edited by Don Reble, May 03 2006