

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
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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), 403422.


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] (* JeanFrançois 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



