A340152 Numbers k such that k and k+1 are both cubefree numbers (A004709).

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

Offset

1,2

Comments

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Leonard Carlitz, On a problem in additive arithmetic (II), The Quarterly Journal of Mathematics, Vol. os-3, No. 1 (1932), pp. 273-290.

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

Subsequence of A004709.

Subsequences: A007674, A328016.

Sequence in context: A354047 A031487 A047422 * A160532 A047305 A032878

Adjacent sequences: A340149 A340150 A340151 * A340153 A340154 A340155

Keyword

nonn,easy

Author

Amiram Eldar, Dec 29 2020

Status

approved