Collectability is another consideration.  To consistently show up in a database of books, manuscripts, maps and ephemera material related to a President has to be desirable enough to make it into the auction rooms, dealer catalogues or bibliographies.
  

There is also the issue of the name being used for another purpose.  George lent his name to Washington, D.C.   If you believe the number of references to Washington D.C. are substantial that will raise George a few notches on the list.  He gets credit for every record that includes Washington anywhere in it.  Therefore thank you Washington Irving.  Grover Cleveland likewise benefits from all things Cleveland, the place, even the pitcher Grover Cleveland Alexander.  James Garfield in the same way benefits from Garfield the Cat.

And there is one more factor, the commonness of the name.   Harrison may have been in office for only 31 days but if Harrison is a common name there may be enough other references to Harrison, such as Harrison, New York and Rex Harrison, in the AED to carry him to the heights of Washington.  Then again, maybe not. 
     

Anyway I hope I am confusing you.  I want to show you the factors while only pretending to help you create your lists.  That is now your job and I calculate the probability that you’ll sequence all thirty-eight presidential last names in the correct order at zero.

Before sending you off into oblivion I’ll provide a little guidance.   The AE Database from which these references have been gathered contained, as of April 23^rd, 2011 3,203,418 records of books, manuscripts, maps and ephemera that have appeared at auction, been listed in important dealer catalogues or described in bibliographies.  Among these records there are 1,124,926 references to these 38 names or an average of 29,603 per name.  Eight of these names have more than 29,603 references, 30 have less.