sum*product = n

[David W. Wilson]

"Robert G. Wilson v" wrote:
> 
> Et al,
> 
>         Using Mathematica, I have tested the sequence up to 7.5*10^7 and
> have found no further numbers which satisfy the criteria.
> 
> Bob.
> 
> "N. J. A. Sloane" wrote:
> 
> > Sol Golomb recently mentioned an old puzzle:
> >
> > find all n such that sum of digits of n times
> > product of digits of n  is equal to n
> >
> > this is a finite sequence which begins 1, 135, 144
> >
> > does any seq fan know of further terms?
> >
> > Neil
> >
> > e g   (1+3+5)*1*3*5) = 135

Try again.

I showed that 1, 135, and 144 are all there are. 

See "Sum-Product Numbers" at mathworld.com.

- Dave Wilson
  Alzheimer's victim