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Differences between two positive cubes in exactly 1 way.
11

%I #13 Mar 19 2020 05:36:54

%S 7,19,26,37,56,61,63,91,98,117,124,127,152,169,189,208,215,217,218,

%T 271,279,296,316,331,335,342,386,387,397,448,469,485,488,504,511,513,

%U 547,602,604,631,657,665,702,784,817,819,866,875,919,936,973,988,992

%N Differences between two positive cubes in exactly 1 way.

%H Robert Israel, <a href="/A014439/b014439.txt">Table of n, a(n) for n = 1..10000</a>

%p N:= 1000: # to get all terms <= N

%p X:= floor(sqrt(N/3)):

%p V:= Vector(N):

%p for x from 2 to X do

%p if x^3 > N then

%p y0:= iroot(x^3-N, 3);

%p if x^3 - y0^3 > N then y0:= y0+1 fi;

%p else y0:= 1 fi;

%p for y from y0 to x-1 do

%p V[x^3 - y^3] := V[x^3 - y^3]+1

%p od

%p od: select(t -> V[t] = 1, [$1..N]); # _Robert Israel_, Dec 11 2015

%t 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 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 nonn

%O 1,1

%A Glen Burch (gburch(AT)erols.com)

%E Corrected and extended by _Don Reble_, Nov 19 2006