(50g) Möbius function (MOB)

[Joe Horn]

The Möbius function, used in number theory, usually written as μ(n) but called MOB(n) here, is defined thus:

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

Examples:

• MOB(32) = 0 because it has a squared prime factor (it can be divided by 2^2).
• MOB(33) = 1 because it is square-free and has an even number of prime factors (3 and 11).
• MOB(30) = -1 because it is square-free and has an odd number of prime factors (2, 3, and 5).

Here is an HP 50g program that returns MOB(n) for any positive integer n.

Code:

\<< 
  IF DUP 1 -
  THEN FACTORS AXL DUP SIZE 2. / 2. + RDM TRAN AXL EVAL 1. +
    IF \PILIST 1. SAME
    THEN SIZE 2. MOD -2. * 1. + R\->I
    ELSE DROP 0
    END
  END
\>>

BYTES: 132.5 #2EE7h