A146169 - OEIS

%I #6 May 12 2013 13:21:37

%S 0,0,17,20,36,48,56,61,65,69,71,73,75,76,77,78,79,80,80,81,81,82,82,

%T 82,83,83,83,83,84,84,84,84

%N Percentage (rounded) of semiprimes <= 2^n which are odd and squarefree.

%C More than 84% of the semiprimes in the interval [4, 2^32] are odd and squarefree. This percentage appears to rise indefinitely as n grows.

%C a(n) = 100 for all n > N. What is the least such N? - _Charles R Greathouse IV_, May 12 2013

%F a(n) = round(A146168(n)/A125527(n)*100)

%e a(5)= 20 since the interval [4, 2^5] contains 10 semiprimes, namely 4,6,9,10,14,15,21,22,25 and 26; and two of those semiprimes, (15 and 21), are odd and squarefree.

%o (PARI) a(n)=my(s,i,N=2^n); forprime(p=2, sqrtint(N), s+=primepi(N\p); i++); s-=i*(i-1)/2; i=primepi(sqrtint(N))+primepi(N/2)-1; round(100*(s-i)/s) \\ _Charles R Greathouse IV_, May 12 2013

%Y Cf. A001358(semiprimes), A125527(Number of semiprimes <= 2^n), A146168(Number of odd squarefree semiprimes < 2^n).

%K nonn

%O 2,3

%A _Washington Bomfim_, Oct 27 2008