A071320 Least of four consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2, k+3} are in A067259.

844, 1681, 8523, 8954, 10050, 10924, 11322, 17404, 19940, 22020, 23762, 24450, 25772, 27547, 30923, 30924, 33172, 34347, 38724, 39050, 39347, 40050, 47673, 47724, 47825, 49147, 54585, 55449, 57474, 58473, 58849, 58867, 59924, 62865

Offset

1,1

Comments

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 0, 1, 4, 57, 555, 5492, 55078, 551443, 5512825, ... . Apparently, the asymptotic density of this sequence exists and equals 0.000551... . - Amiram Eldar, Jan 18 2023

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Michael De Vlieger)

Formula

A051903(k) = A051903(k+1) = A051903(k+2) = A051903(k+3) = 2 when k is a term.

Example

k = 844 is a term since 844 = 2^2*211, k+1 = 845 = 5*13^2, k+2 = 846 = 2*3^2*47, and k+4 = 847 = 7*11^2.

Mathematica

With[{s = Select[Range[10^5], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ SequencePosition[t, {1, 1, 1}][[All, 1]]]@ Differences@ s] (* Michael De Vlieger, Jul 30 2017 *)

Crossrefs

Subsequence of A067259, A071318 and A071319.

Cf. A051903, A063528.

Sequence in context: A038013 A334183 A078144 * A338628 A323253 A160212

Adjacent sequences: A071317 A071318 A071319 * A071321 A071322 A071323

Keyword

nonn

Author

Labos Elemer, May 29 2002

Status

approved