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A096300 Number of positive integers <= n with no prime factor > log(n). 1
1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Table of n, a(n) for n=1..75.

A. Granville, On positive integers <= x with prime factors <= t log x, Number Theory and Applications (ed. R.A Mollin), (Kluwer, NATO ASI, 1989), 403-422.

FORMULA

From Charlie Neder, Feb 08 2019: (Start)

a(n) = A000012(n) for 0 < n <= floor(e^2) = 7,

       A070939(n) for 7 < n <= floor(e^3) = 20,

       A071521(n) for 20 < n <= floor(e^5) = 148,

       A071520(n) for 148 < n <= floor(e^7) = 1096,

       A071604(n) for 1096 < n <= floor(e^11) = 59874,

and so on. (End)

MATHEMATICA

a[n_] := Select[Range[n], FactorInteger[#][[-1, 1]] <= Log[n]&] // Length;

a[1] = a[2] = 1;

a /@ Range[75] (* Jean-Fran├žois Alcover, May 17 2020 *)

PROG

(PARI) a(n)=local(s, t); s=0; for(k=1, n, f=factor(k); t=0; for(l=1, matsize(f)[1], if(f[l, 1]>log(n), t=1; break)); s=s+!t); s

CROSSREFS

Sequence in context: A290205 A066014 A080678 * A333534 A035672 A113472

Adjacent sequences:  A096297 A096298 A096299 * A096301 A096302 A096303

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Aug 03 2004

STATUS

approved

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Last modified August 5 17:46 EDT 2021. Contains 346488 sequences. (Running on oeis4.)