Sum-product numbers

frusso frusso at
Tue Oct 12 09:05:37 CEST 1999

the sequence has been created by me about one year ago. 
So I think that no reference exist (at least for what I know).
You can find other similar sequences in EIS.

Rgds.  Felice

-----Original Message-----
From: Eric W. Weisstein [mailto:eww at]
Sent: Monday, October 11, 1999 7:14 PM
To: Sequence Fans Mailing List
Subject: Sum-product numbers

Does anyone have a proof on the (non)existence of any more sum-product
numbers, i.e., numbers n s.t. n = (product of digits of n) x (sum of
digits of n);  
Other than 1, 135, 144, there are no others < 10^9.  The sequence is known
to be finite
and it seems likely that clever arguments based on divisibility might be
able to establish if any more such numbers actually exist.


P.S. Does anyone have a reference where these first appeared?

* Eric W. Weisstein                                                *
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