A349235 -id:A349235 - cp's OEIS frontend

A349233 Numbers k such that k and k+2 are consecutive cubefree numbers.

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

Amiram Eldar, Nov 11 2021

nonn

The asymptotic density of this sequence is 0.142325864924778... (Mossinghoff et al., 2021).

			7 is a term since 7 and 7 + 2 = 9 = 3^2 are cubefree, and 7 + 1 = 8 = 2^3 is not.

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

Cf. A004709, A046099, A340152, A349234, A349235.

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[400], Boole[cubeFreeQ /@ (# + {0, 1, 2})] == {1, 0, 1} &]

A349234 Numbers k such that k and k+3 are consecutive cubefree numbers.

Original entry on oeis.org

79, 134, 295, 342, 350, 374, 511, 566, 623, 727, 782, 943, 998, 1159, 1214, 1430, 1591, 1623, 1646, 1807, 1862, 2023, 2078, 2239, 2294, 2374, 2399, 2455, 2510, 2623, 2671, 2726, 2887, 2942, 3086, 3103, 3158, 3319, 3374, 3428, 3535, 3590, 3623, 3751, 3806, 3967

Offset: 1

Amiram Eldar, Nov 11 2021

nonn

The asymptotic density of this sequence is 0.0123046264590258... (Mossinghoff et al., 2021).

			79 is a term since 79 and 79 + 3 = 82 = 2*41 are cubefree, and 79 + 1 = 80 = 2^4*5 and 79 + 2 = 81 = 3^4 are not.

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

Cf. A004709, A046099, A340152, A349233, A349235.

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[4000], Boole[cubeFreeQ /@ (# + Range[0, 3])] == {1, 0, 0, 1} &]
SequencePosition[Table[If[Max[FactorInteger[n][[All,2]]]<3,1,0],{n,4000}],{1,0,0,1}][[All,1]] (* Harvey P. Dale, May 08 2022 *)

cp's OEIS Frontend

A349233 Numbers k such that k and k+2 are consecutive cubefree numbers.

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