semiprime

A composite number which is the product of two (possibly equal) primes is called semiprime. Such numbers are sometimes also called 2-almost primes. For example:

• 1 is not a semiprime because it is not a composite number or a prime,

• 2 is not a semiprime, as it is a prime,

• 4 is a semiprime, since $4=2\cdot 2$,

• 8 is not a semiprime, since it is a product of three primes ($8=2\cdot 2\cdot 2$),

• 2003 is not a semiprime, as it is a prime,

• 2005 is a semiprime, since $2005=5\cdot 401$,

• 2007 is not a semiprime, since it is a product of three primes ($2007=3\cdot 3\cdot 223$).

The first few semiprimes are $4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,\mathrm{\dots }$ (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001358Sloane’s sequence A001358). The Moebius function $\mu (n)$ for semiprimes can be only equal to 0 or 1. If we form an integer sequence of values of $\mu (n)$ for semiprimes we get a binary sequence: $0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,\mathrm{\dots }$. (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=072165Sloane’s sequence A072165).

All the squares of primes are also semiprimes. The first few squares of primes are then $4,9,25,49,121,169,289,361,529,841,961,1369,1681,1849,2209,2809,3481,3721,4489,5041,\mathrm{\dots }$. (http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=001248Sloane’s sequence A001248). The Moebius function $\mu (n)$ for the squares of primes is always equal to 0 as it is equal to 0 for all squares.