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
Keywords
Examples
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).
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..400
Programs
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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
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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 *) -
PARI
for(n=1, 1e5, f = factor(n)[, 2]; if((#f == 0) || vecmax(f) < 3, if(ispower(n + 1, 3), print1(n, ", "))));
Comments