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

1,1

Links

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

Example

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

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 *)

Prog

(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) }

Crossrefs

Cf. A003336, A088728.

Sequence in context: A053826 A351267 A184982 * A321560 A034678 A065960

Adjacent sequences: A088684 A088685 A088686 * A088688 A088689 A088690

Keyword

nonn

Author

Cino Hilliard, Nov 22 2003

Extensions

Edited by Don Reble, May 03 2006

Status

approved