A349233 -id:A349233 - cp's OEIS frontend

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

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 *)

A349235 Numbers k such that k and k+4 are consecutive cubefree numbers.

Original entry on oeis.org

1374, 4373, 4911, 5749, 6857, 13309, 13374, 16118, 21247, 24351, 25622, 28374, 31373, 32749, 33613, 40471, 41741, 48247, 49623, 49733, 52622, 55374, 57966, 58373, 59749, 75247, 76623, 79622, 82374, 85373, 86749, 90206, 94470, 98439, 102247, 103623, 106622, 107701

Offset: 1

Amiram Eldar, Nov 11 2021

nonn

The asymptotic density of this sequence is 0.000379098586237504... (Mossinghoff et al., 2021).

			1374 is a term since 1374 = 2*3*229 and 1374 + 4 = 1378 = 2*13*53 are cubefree, and 1374 + 1 = 1375 = 5^3*11, 1374 + 2 = 1376 = 2^5*43 and 1374 + 3 = 1377 = 3^4*17 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, A349234.

cubeFreeQ[n_] := AllTrue[FactorInteger[n][[;; , 2]], # < 3 &]; Select[Range[10^5], Boole[cubeFreeQ /@ (# + Range[0, 4])] == {1, 0, 0, 0, 1} &]

cp's OEIS Frontend

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

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