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A014439 Differences between two positive cubes in exactly 1 way.

%I A014439 #13 Mar 19 2020 05:36:54
%S A014439 7,19,26,37,56,61,63,91,98,117,124,127,152,169,189,208,215,217,218,
%T A014439 271,279,296,316,331,335,342,386,387,397,448,469,485,488,504,511,513,
%U A014439 547,602,604,631,657,665,702,784,817,819,866,875,919,936,973,988,992
%N A014439 Differences between two positive cubes in exactly 1 way.
%H A014439 Robert Israel, <a href="/A014439/b014439.txt">Table of n, a(n) for n = 1..10000</a>
%p A014439 N:= 1000: # to get all terms <= N
%p A014439 X:= floor(sqrt(N/3)):
%p A014439 V:= Vector(N):
%p A014439 for x from 2 to X do
%p A014439   if x^3 > N then
%p A014439      y0:= iroot(x^3-N, 3);
%p A014439      if x^3 - y0^3 > N then y0:= y0+1 fi;
%p A014439   else y0:= 1 fi;
%p A014439   for y from y0 to x-1 do
%p A014439      V[x^3 - y^3] := V[x^3 - y^3]+1
%p A014439   od
%p A014439 od: select(t -> V[t] = 1, [$1..N]); # _Robert Israel_, Dec 11 2015
%t A014439 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 *)
%Y A014439 Cf. A000578, A038593, A181123, A034179 (more than one way), A014440 (exactly two ways), A265625 (more than two ways), A014441 (exactly three ways), A333376, A333377.
%K A014439 nonn
%O A014439 1,1
%A A014439 Glen Burch (gburch(AT)erols.com)
%E A014439 Corrected and extended by _Don Reble_, Nov 19 2006