The classical Möbius function: μ(n) is an important multiplicative function in number theory and combinatorics.

There are several ways to implement a Möbius function.

A fairly straightforward method is to find the prime factors of a positive integer n, then define μ(n) based on the sum of the primitive factors. It has the values {−1, 0, 1} depending on the factorization of n:

 μ(1) is defined to be 1.
 μ(n) = 1 if n is a square-free positive integer with an even number of prime factors.
 μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors.
 μ(n) = 0 if n has a squared prime factor.


Task

 Write a routine (function, procedure, whatever) μ(n) to find the Möbius number for a positive integer n.
 Use that routine to find and display here, on this page, at least the first 99 terms in a grid layout. (Not just one long line or column of numbers.)


See also

 Wikipedia: Möbius function


Related Tasks

 Mertens function


function mobius( n as uinteger ) as integer
    if n = 1 then return 1
    for d as uinteger = 2 to int(sqr(n))
        if n mod d = 0 then 
            if n mod (d*d) = 0 then return 0
            return -mobius(n/d)
        end if
    next d
    return -1
end function
 
dim as string outstr = " .     "
for i as uinteger = 1 to 200
    if mobius(i)>=0 then outstr += " "
    outstr += str(mobius(i))+"     "
    if i mod 10 = 9 then 
        print outstr
        outstr = ""
    end if
next i