OFFSET
1,1
COMMENTS
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
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Feb 14 2016
STATUS
approved