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

Author

Labos Elemer, May 29 2002

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Subsequence of A067259, A071318 and A071319.

Cf. A051903, A063528.

Programs

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 *)

Formula

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