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A349233
Numbers k such that k and k+2 are consecutive cubefree numbers.
3
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 11 2021
STATUS
approved