> I have a simple function that (like your example) can compute things
> for size=2.  I am trying to figure out how to generalize to arbitrary
> size.

Here's an example of how you can do it in Sage:

sage: a = factor(2*3*3*5*7*13);a
2 * 3^2 * 5 * 7 * 13
sage: b = sum([ [f]*mult for f,mult in a], []); b
[2, 3, 3, 5, 7, 13]
sage: size = 3
sage: c = [ [ prod(sp) for sp in osps ] for osps in
OrderedSetPartitions(b, size) ]

where c is your list of "multiplicative partitions".  If you don't
care about order, just replace OrderedSetPartitions with
SetPartitions.

--Mike

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