Well, it can not be exactly the same formula because the J one finds semiprimes less than n while the MathWorld one finds those less than or equal to n . I derived the J computation before I saw the MathWorld one and saw that they are very similar.
As a mathematician, do you find the MathWorld formula? pi<sup>(2)</sup>(x)=sigma(k=1,pi(sqrt(n))) [pi(n/p<sub>k</sub>-k+1] The following are a list questions I have: - pi<sup>(2)</pi>(x) is non-standard, at least unusual. Superscript usually means exponentiation. - x should be n (I assume this is a typo) - Square brackets sometimes mean the nearest integer. In this case I think it just denotes grouping; the author could have used parens. In J, with the same reasoning, one readily derives a computation that produces the actual semiprimes. That is an illustration of the power of J in dealing with arrays. ----- Original Message ----- From: John Randall <[EMAIL PROTECTED]> Date: Saturday, April 5, 2008 6:06 Subject: Re: [Jgeneral] How readable is J? To: General forum <[email protected]> > Roger Hui wrote: > > > The MathWorld page doesn't give the derivation > > I believe the MathWorld formula is the same as the J derivation. > > Primes are indexed starting at 1. You iterate over primes p_k whose > square is less than or equal to n. The term pi(n/p_k) > counts primes q > such that n>:(p_k)*q . You subtract (k-1) to count only primes q with > p_k<q . > > Best wishes, > > John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
