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)
	if n = 1 then return 1
	for d = 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
 
outstr$ = " .   "
for i = 1 to 200
	if mobius(i) >= 0 then outstr$ += " "
	outstr$ += string(mobius(i)) + "   "
	if i mod 10 = 9 then
		print outstr$
		outstr$ = ""
	end if
next i
end