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

2,3

Comments

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

Links

Table of n, a(n) for n=2..33.

Formula

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A340046 A116037 A081643 * A218864 A045020 A069961

Adjacent sequences: A146166 A146167 A146168 * A146170 A146171 A146172

Keyword

nonn

Author

Washington Bomfim, Oct 27 2008

Status

approved