A014439 Differences between two positive cubes in exactly 1 way.

7, 19, 26, 37, 56, 61, 63, 91, 98, 117, 124, 127, 152, 169, 189, 208, 215, 217, 218, 271, 279, 296, 316, 331, 335, 342, 386, 387, 397, 448, 469, 485, 488, 504, 511, 513, 547, 602, 604, 631, 657, 665, 702, 784, 817, 819, 866, 875, 919, 936, 973, 988, 992

Offset: 1

Author

Glen Burch (gburch(AT)erols.com)

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000578, A038593, A181123, A034179 (more than one way), A014440 (exactly two ways), A265625 (more than two ways), A014441 (exactly three ways), A333376, A333377.

Programs

Maple

N:= 1000: # to get all terms <= N
X:= floor(sqrt(N/3)):
V:= Vector(N):
for x from 2 to X do
  if x^3 > N then
     y0:= iroot(x^3-N, 3);
     if x^3 - y0^3 > N then y0:= y0+1 fi;
  else y0:= 1 fi;
  for y from y0 to x-1 do
     V[x^3 - y^3] := V[x^3 - y^3]+1
  od
od: select(t -> V[t] = 1, [$1..N]); # Robert Israel, Dec 11 2015

Mathematica

r = 992; p = 3; Sort@Drop[Flatten@Select[Tally@Reap[Do[n = i^p - j^p; If[n <= r, Sow[n]], {i, Ceiling[(r/p)^(1/(p - 1))]}, {j, i}]][[2, 1]], #[[2]] == 1 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Corrected and extended by Don Reble, Nov 19 2006