A071319 First of 3 consecutive numbers which are cubefree and not squarefree, i.e., numbers k such that {k, k+1, k+2} are in A067259.

98, 475, 548, 603, 724, 844, 845, 1274, 1420, 1681, 1682, 1924, 2275, 2523, 2890, 3283, 3474, 3548, 3626, 3716, 4148, 4203, 4418, 4475, 4850, 4923, 4948, 5202, 5274, 5490, 5524, 5634, 5948, 6650, 6811, 6956, 7299, 7324, 7442, 7514, 7675, 8107, 8348

Offset

1,1

Comments

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 0, 1, 7, 55, 570, 5628, 56174, 562151, 5621119, 56209006, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00562... . - Amiram Eldar, Jan 18 2023

The asymptotic density of this sequence is Product_{p prime} (1 - 3/p^3) - 3 * Product_{p prime} (1 - 1/p^2 - 2/p^3) + 3 * Product_{p prime} (1 - 2/p^2 - 1/p^3) - Product_{p prime} (1 - 3/p^2) = 0.0056209097169531390208... . - Amiram Eldar, Jan 12 2024

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

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

Example

98 is a term since 98 = 2*7^2, 99 = 3^2*11, and 100 = 2^2*5^2.

Mathematica

With[{s = Select[Range[10^4], And[MemberQ[#, 2], FreeQ[#, k_ /; k > 2]] &@ FactorInteger[#][[All, -1]] &]}, Function[t, Part[s, #] &@ SequencePosition[t, {1, 1}][[All, 1]]]@ Differences@ s] (* Michael De Vlieger, Jul 30 2017 *)

Prog

(PARI) isok(n) = (n>1) && (vecmax(factor(n)[, 2])==2) && (vecmax(factor(n+1)[, 2])==2) && (vecmax(factor(n+2)[, 2])==2); \\ Michel Marcus, Aug 02 2017

Crossrefs

Subsequence of A067259 and A071318.

Cf. A051903, A063528.

Sequence in context: A306214 A160828 A158129 * A263040 A263033 A239173

Adjacent sequences: A071316 A071317 A071318 * A071320 A071321 A071322

Keyword

nonn

Author

Labos Elemer, May 29 2002

Status

approved