A349233 Numbers k such that k and k+2 are consecutive cubefree numbers.

7, 15, 23, 26, 31, 39, 47, 53, 55, 63, 71, 87, 95, 103, 107, 111, 119, 124, 127, 143, 151, 159, 161, 167, 175, 183, 188, 191, 199, 207, 215, 223, 231, 239, 242, 247, 249, 255, 263, 269, 271, 279, 287, 303, 311, 319, 323, 327, 335, 359, 367, 377, 383, 391, 399

Offset

1,1

Comments

The asymptotic density of this sequence is 0.142325864924778... (Mossinghoff et al., 2021).

Links

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

Michael J. Mossinghoff, Tomás Oliveira e Silva, and Tim Trudgian, The distribution of k-free numbers, Mathematics of Computation, Vol. 90, No. 328 (2021), pp. 907-929; arXiv preprint, arXiv:1912.04972 [math.NT], 2019-2020.

Example

7 is a term since 7 and 7 + 2 = 9 = 3^2 are cubefree, and 7 + 1 = 8 = 2^3 is not.

Mathematica

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[400], Boole[cubeFreeQ /@ (# + {0, 1, 2})] == {1, 0, 1} &]

Crossrefs

Cf. A004709, A046099, A340152, A349234, A349235.

Sequence in context: A041935 A041092 A367907 * A335512 A369375 A004215

Adjacent sequences: A349230 A349231 A349232 * A349234 A349235 A349236

Keyword

nonn

Author

Amiram Eldar, Nov 11 2021

Status

approved