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A328016 Numbers k such that k, k+1, ... k+6 are all cubefree (A004709). 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A260477 A275543 A111733

Adjacent sequences:  A328013 A328014 A328015 * A328017 A328018 A328019

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Oct 01 2019

STATUS

approved

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Last modified February 22 23:44 EST 2020. Contains 332157 sequences. (Running on oeis4.)