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A096300 Number of positive integers <= n with no prime factor > log(n).

%I A096300 #15 May 17 2020 07:29:59
%S A096300 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,
%T A096300 12,12,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,
%U A096300 15,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18,18,18,18
%N A096300 Number of positive integers <= n with no prime factor > log(n).
%H A096300 A. Granville, <a href="http://cr.yp.to/bib/1989/granville.ps">On positive integers <= x with prime factors <= t log x</a>, Number Theory and Applications (ed. R.A Mollin), (Kluwer, NATO ASI, 1989), 403-422.
%F A096300 From _Charlie Neder_, Feb 08 2019: (Start)
%F A096300 a(n) = A000012(n) for 0 < n <= floor(e^2) = 7,
%F A096300        A070939(n) for 7 < n <= floor(e^3) = 20,
%F A096300        A071521(n) for 20 < n <= floor(e^5) = 148,
%F A096300        A071520(n) for 148 < n <= floor(e^7) = 1096,
%F A096300        A071604(n) for 1096 < n <= floor(e^11) = 59874,
%F A096300 and so on. (End)
%t A096300 a[n_] := Select[Range[n], FactorInteger[#][[-1, 1]] <= Log[n]&] // Length;
%t A096300 a[1] = a[2] = 1;
%t A096300 a /@ Range[75] (* _Jean-François Alcover_, May 17 2020 *)
%o A096300 (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
%K A096300 nonn,easy
%O A096300 1,8
%A A096300 _Ralf Stephan_, Aug 03 2004