Even Part

The even part  of a positive integer  is defined by

where  is the exponent of the exact power of 2 dividing . The values for , 2, ..., are 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, ... (OEIS A006519). The even part function can be implemented in the Wolfram Language as

  EvenPart[0]:=1
  EvenPart[n_Integer]:=2^IntegerExponent[n,2]

REFERENCES:

Sloane, N. J. A. Sequence A006519/M0162 in "The On-Line Encyclopedia of Integer Sequences."