Infinitely Many Rhondas

A positive integer N is a "Rhonda Number" if for some positive integer 
B the product of the base-B digits of N equals B times the sum of the 
prime factors of N.  The smallest example is 560, which is a Rhonda 
Number to the base 12.

PROPOSITION:  There are infinitely many Rhonda Numbers.

PROOF:  Let sopf(n) denote the sum of the prime factors of n.  Then 
for any integer m>5 the number N = km(m+1)(2m+1)^2 is a Rhonda Number 
to the base B = 2km(m+1), where k is any integer such that

         sopf(k) = m(m+1) - sopf(m) - sopf(m+1) - 2 sopf(2m+1)

We are assured the existence of at least one k satisfying this 
equation, because sopf(n) <= n, which implies the negative terms on 
the right side combined can be no larger than 6m+3, which is smaller 
than m(m+1) for m>5.  Therefore, the above expression for sopf(k) 
is a positive integer u. If u is even then u=2s and k=2^s satisfies 
the equation.  If u is odd, then u=2s+3 and k=3(2^s) satisfies the 
equation.

The digits of N in the base B are d0 = km(m+1) and d1 = 2m(m+1), so 
the product of these digits is 2k(m^2)(m+1)^2.  Also, since the sopf 
function is additive, we have

     sopf(N) = sopf(k) + sopf(m) + sopf(m+1) + 2 sopf(2m+1)

             =  m(m+1)

so B times sopf(N) equals 2k(m^2)(m+1)^2, which equals the product of 
the base-B digits as required.

In general, for each value of m there correspond several distinct 
Rhonda Numbers, one for each prime partition of sopf(k).  The smallest 
example of a Rhonda Number given by this construction is 28392 
relative to the base 336 (corresponding to m=6 and k=4).

By the way, the number 140800 has an interesting property that I've 
never heard anyone mention.  The digits of this number when written in 
each of several bases are shown below:
                                      
            Base         d2    d1    d0

             198          3   117    22
             832              169   192
            1200              117   400
            1540               91   660
            1728               81   832
            2024               69  1144
            2360               59  1560
            2720               51  2080

In each case the product of the digits divided by the base equals 
39, which also happens to be the sum of the prime factors of 140800.  
Does anyone know of a number with this property relative to more 
than 8 distinct bases?