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

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

Author

Amiram Eldar, Nov 11 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A004709, A046099, A340152, A349233, A349234.

Programs

Mathematica

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