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Task/M-bius-function/00-TASK.txt

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+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:
+:*; [[wp:Möbius function|Wikipedia: Möbius function]]
+
+
+;Related Tasks:
+:*; [[Mertens function]]
+<br><br>
+