A280892 Squareful numbers with both neighbors squarefree.

4, 12, 16, 18, 20, 32, 36, 40, 52, 54, 56, 60, 68, 72, 84, 88, 90, 92, 96, 104, 108, 112, 128, 132, 140, 144, 150, 156, 160, 162, 164, 180, 184, 192, 196, 198, 200, 204, 212, 216, 220, 228, 232, 234, 236, 240, 248, 250, 252, 256, 264, 268, 270, 272, 284, 292, 294, 300, 304, 306, 308, 312

Offset

1,1

Comments

Subsequence of A013929 and A067874.

The asymptotic density of this sequence is Product_{p prime} (1 - 2/p^2) - Product_{p prime} (1 - 3/p^2) = 0.197147118033435... (Mossinghoff et al., 2021). - Amiram Eldar, Nov 11 2021, Mar 21 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

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

4 is in this sequence because 4 = 2^2 is nonsquarefree and both 4 - 1 = 3 and 4 + 1 = 5 are squarefree.

Mathematica

Mean/@SequencePosition[Table[If[SquareFreeQ[n], 1, 0], {n, 400}], {1, 0, 1}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 19 2020 *)

Prog

(Magma) [n: n in [2..300] | not IsSquarefree(n) and IsSquarefree(n-1) and IsSquarefree(n+1)];
(PARI) isok(n) = !issquarefree(n) && issquarefree(n-1) && issquarefree(n+1); \\ Michel Marcus, Jun 18 2017

Crossrefs

Cf. A005117, A013929, A067874, A228649, A272799, A281192.

Cf. A065474, A206256.

Sequence in context: A144976 A119622 A367909 * A328840 A255411 A340929

Adjacent sequences: A280889 A280890 A280891 * A280893 A280894 A280895

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jan 16 2017

Extensions

Definition corrected by Jon E. Schoenfield, Jun 18 2017

Status

approved