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A328016
Numbers k such that k, k+1, ... k+6 are all cubefree (A004709).
4
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Oct 01 2019
STATUS
approved