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A268861 Cubefree numbers n such that n + 1 is a perfect cube. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Intersection of A004709 and A068601. - Michel Marcus, Feb 15 2016
LINKS
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
Sequence in context: A135300 A024001 A068601 * A221793 A299282 A269700
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Feb 14 2016
STATUS
approved

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Last modified April 13 15:44 EDT 2024. Contains 371644 sequences. (Running on oeis4.)