Returns the cardinality of the multiplicative partition set for an integer (in PARI/GP)

mnumbpart.gp

/*
Returns the number of multiplicative partitions of integer n
Ref: https://oeis.org/A001055 
	 https://oeis.org/A162247
	 https://oeis.org/A162247/a162247.txt

Inputs:
	n: Non-negative integer
	m: Maximum factor (optional)
	
Output:
	V: Vector of multiplicative partitions of n
	
Example:
mnumbpart(60) = 11

Written by: John Peach 29-Dec-2020          
Modified from fcnt function by Michael B. Porter (Oct 29 2009), https://oeis.org/A001055         

*/

mnumbpart(n,m = n) = 
{
	local(s);
	s=0;
	if(n==1,s=1,
		fordiv(n,d,if(d>1&d<=m,s=s+mnumbpart(n/d,d)))
	);
	return(s);
}