

A340152


Numbers k such that k and k+1 are both cubefree numbers (A004709).


10



1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 25, 28, 29, 30, 33, 34, 35, 36, 37, 38, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 73, 74, 75, 76, 77, 78, 82, 83, 84, 85, 86, 89, 90, 91, 92, 93, 94
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OFFSET

1,2


COMMENTS

The asymptotic density of this sequence is Product_{p prime} (1  2/p^3) = 0.6768927370... (A340153) (Carlitz, 1932).


LINKS



EXAMPLE

1 is a term since both 1 and 2 are cubefree numbers.
7 is not a term since 7+1 = 8 = 2^3 is not cubefree.


MATHEMATICA

cubefreeQ[n_] := Max @ FactorInteger[n][[;; , 2]] < 3; Select[Range[100], cubefreeQ[#] && cubefreeQ[# + 1] &]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



