%I #13 Oct 11 2021 16:49:49

%S 7,26,63,124,215,342,511,1330,1727,2196,2743,3374,4095,7999,9260,

%T 10647,12166,13823,17575,19682,24388,26999,29790,32767,39303,42874,

%U 46655,54871,59318,63999,74087,79506,85183,91124,103822,110591,124999,132650,140607,148876

%N Cubefree numbers n such that n + 1 is a perfect cube.

%C Intersection of A004709 and A068601. - _Michel Marcus_, Feb 15 2016

%H K. D. Bajpai, <a href="/A268861/b268861.txt">Table of n, a(n) for n = 1..400</a>

%e a(2) = 26 = 2 * 13 that is cubefree. 26 + 1 = 27 = 3^3 (perfect cube).

%e a(4) = 124 = 2 * 2 * 31 that is cubefree. 124 + 1 = 125 = 5^3 (perfect cube).

%p cubefree:= proc(n) local t;

%p max(seq(t[2],t=ifactors(n)[2])) <= 2

%p end proc:

%p select(cubefree, [seq(i^3-1,i=2..100)]); # _Robert Israel_, Mar 03 2016

%t Select[Range[150000], FreeQ[FactorInteger[#], {_, k_ /; k > 2}] && IntegerQ[CubeRoot[# + 1]] &]

%t Select[Range[2,70]^3,Max[FactorInteger[#-1][[All,2]]]<3&]-1 (* _Harvey P. Dale_, Oct 11 2021 *)

%o (PARI) for(n=1, 1e5, f = factor(n)[, 2]; if((#f == 0) || vecmax(f) < 3, if(ispower(n + 1, 3), print1(n, ", "))));

%Y Cf. A004709, A068601, A121628, A221793, A268752.

%K nonn

%O 1,1

%A _K. D. Bajpai_, Feb 14 2016