A polynomial of the form: 
, for 
, is said to be natural factorable if it can be factored into products of first degree binomials: 
, where, 
and 
are all natural numbers (i.e. integers that are 
).
, for , is said to be natural factorable if it can be factored into products of first degree binomials: , where, and are all natural numbers (i.e. integers that are ).Given an integer a, write a function that counts the number of all possible natural factorable polynomials that can be formed, wherein 
.
.For example, when 
, the are 7 possible natural factorable polynomials, namely:
, the are 7 possible natural factorable polynomials, namely:
;
;
;
;
; and
Therefore the function output should be 7.
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