A146168 -id:A146168 - cp's OEIS frontend

A146169 Percentage (rounded) of semiprimes <= 2^n which are odd and squarefree.

0, 0, 17, 20, 36, 48, 56, 61, 65, 69, 71, 73, 75, 76, 77, 78, 79, 80, 80, 81, 81, 82, 82, 82, 83, 83, 83, 83, 84, 84, 84, 84

Offset: 2

Washington Bomfim, Oct 27 2008

nonn

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.

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

			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.

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

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

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

A146170 Percentage (rounded) of odd numbers < 2^n which are primes or squarefree semiprimes.

Original entry on oeis.org

0, 50, 75, 75, 75, 78, 78, 77, 75, 72, 70, 66, 64, 61, 59, 57, 55, 53, 51, 49, 48, 46, 45, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34

Offset: 1

Washington Bomfim, Oct 27 2008

nonn

			a(4)=75 because 75% of the 2^3 numbers 1, 3, 5, 7, 9, 11, 13 and 15 are primes or squarefree semiprimes.

Cf. A001358(semiprimes), A007053(Number of primes <= 2^n), A146168(Number of odd squarefree semiprimes < 2^n).

a(n) = round((A146168(n)+A007053(n)-1)/(2^(n-1))*100).

cp's OEIS Frontend

A146169 Percentage (rounded) of semiprimes <= 2^n which are odd and squarefree.

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