cp's OEIS Frontend

A091372 Number of numbers <= n having more prime factors than the value of their smallest prime factor.

%I A091372 #16 Jul 06 2016 16:30:04
%S A091372 0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,3,3,4,4,5,5,5,5,6,6,6,6,7,7,8,8,9,9,9,
%T A091372 9,10,10,10,10,11,11,12,12,13,13,13,13,14,14,15,15,16,16,17,17,18,18,
%U A091372 18,18,19,19,19,19,20,20,21,21,22,22,23,23,24,24,24,24,25,25,26,26,27
%N A091372 Number of numbers <= n having more prime factors than the value of their smallest prime factor.
%C A091372 a(n) = #{m: A001222(m)>A020639(m), m<=n};
%C A091372 a(n) + A091373(n) + A091374(n) = n.
%H A091372 Michael De Vlieger, <a href="/A091372/b091372.txt">Table of n, a(n) for n = 1..10000</a>
%F A091372 For any k < 1, a(n) > kn for large enough k. For example, a(n) > n/2 for n > 26474. - _Charles R Greathouse IV_, Jul 06 2016
%t A091372 Accumulate@ Boole@ Map[Length@ Flatten[Table[#1, {#2}] & @@@ #] > #[[1, 1]] &@ FactorInteger@ # &, Range@ 80] (* _Michael De Vlieger_, Jul 06 2016 *)
%o A091372 (PARI) a(n)=sum(k=8,n, bigomega(k) > factor(k)[1,1]) \\ _Charles R Greathouse IV_, Jul 06 2016
%o A091372 (PARI) first(n)=my(v=vector(n),s); for(k=8,n, v[k] = s += bigomega(k) > factor(k)[1,1]); v \\ _Charles R Greathouse IV_, Jul 06 2016
%Y A091372 Cf. A091375, A091371.
%K A091372 nonn
%O A091372 1,12
%A A091372 _Reinhard Zumkeller_, Jan 04 2004