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A088687
Numbers that can be represented as j^4 + k^4, with 0 < j < k, in exactly one way.
11
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
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
Sequence in context: A053826 A351267 A184982 * A321560 A034678 A065960
KEYWORD
nonn
AUTHOR
Cino Hilliard, Nov 22 2003
EXTENSIONS
Edited by Don Reble, May 03 2006
STATUS
approved