A038593 Differences between positive cubes in 1, 2 or 3 ways: union of A014439, A014440 and A014441.

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, 721, 728, 784, 817, 819, 866, 875, 919, 936, 973, 988

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Links

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

Crossrefs

Cf. A038594, A038595, A038596, A038597, A038598.

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] <= 3 and V[t]>=1, [$1..N]); # Robert Israel, Dec 10 2015

Mathematica

r = 988; 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]], 0 < #[[2]] < 4 &], {2, -1, 2}] (* Arkadiusz Wesolowski, Dec 10 2015 *)

Extensions

Corrected by Don Reble, Nov 19 2006