A328016 Numbers k such that k, k+1, ... k+6 are all cubefree (A004709).

1, 9, 17, 33, 41, 57, 65, 73, 89, 97, 113, 137, 145, 153, 169, 177, 193, 201, 209, 217, 225, 233, 257, 273, 281, 289, 305, 313, 329, 353, 361, 385, 393, 409, 417, 425, 433, 441, 449, 465, 473, 489, 505, 521, 529, 545, 553, 569, 577, 585, 601, 609, 633, 641, 649, 657

Offset

1,2

Comments

There cannot be 8 consecutive cubefree numbers since one of them must be divisible by 8 = 2^3.

All the terms are congruent to 1 mod 8.

The asymptotic density of this sequence is A328017.

Links

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

Leon Mirsky, Arithmetical pattern problems relating to divisibility by rth powers, Proceedings of the London Mathematical Society, Vol. s2-50, No. 1 (1949), pp. 497-508.

Example

9 is in the sequence since the numbers 9, 10, ... 15 are all cubefree.

Mathematica

cubeFreeQ[n_] := FreeQ[FactorInteger[n], {_, k_ /; k > 2}]; aQ[n_] := AllTrue[n + Range[0, 6], cubeFreeQ]; Select[Range[650], aQ]

Crossrefs

Cf. A004709, A007675, A194002, A325058, A328017.

Sequence in context: A014004 A090994 A164887 * A335796 A260477 A275543

Adjacent sequences: A328013 A328014 A328015 * A328017 A328018 A328019

Keyword

nonn,easy

Author

Amiram Eldar, Oct 01 2019

Status

approved