A268861 Cubefree numbers n such that n + 1 is a perfect cube.

7, 26, 63, 124, 215, 342, 511, 1330, 1727, 2196, 2743, 3374, 4095, 7999, 9260, 10647, 12166, 13823, 17575, 19682, 24388, 26999, 29790, 32767, 39303, 42874, 46655, 54871, 59318, 63999, 74087, 79506, 85183, 91124, 103822, 110591, 124999, 132650, 140607, 148876

Offset

1,1

Comments

Intersection of A004709 and A068601. - Michel Marcus, Feb 15 2016

Links

K. D. Bajpai, Table of n, a(n) for n = 1..400

Example

a(2) = 26 = 2 * 13 that is cubefree. 26 + 1 = 27 = 3^3 (perfect cube).
a(4) = 124 = 2 * 2 * 31 that is cubefree. 124 + 1 = 125 = 5^3 (perfect cube).

Maple

cubefree:= proc(n) local t;
  max(seq(t[2], t=ifactors(n)[2])) <= 2
end proc:
select(cubefree, [seq(i^3-1, i=2..100)]); # Robert Israel, Mar 03 2016

Mathematica

Select[Range[150000], FreeQ[FactorInteger[#], {_, k_ /; k > 2}] && IntegerQ[CubeRoot[# + 1]] &]
Select[Range[2, 70]^3, Max[FactorInteger[#-1][[All, 2]]]<3&]-1 (* Harvey P. Dale, Oct 11 2021 *)

Prog

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

Crossrefs

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

Sequence in context: A135300 A024001 A068601 * A221793 A299282 A269700

Adjacent sequences: A268858 A268859 A268860 * A268862 A268863 A268864

Keyword

nonn

Author

K. D. Bajpai, Feb 14 2016

Status

approved