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Even Part


EvenPart

The even part Ev(n) of a positive integer n is defined by

 Ev(n)=2^(b(n)),

where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 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]

See also

Greatest Dividing Exponent, Odd Part

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References

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

Referenced on Wolfram|Alpha

Even Part

Cite this as:

Weisstein, Eric W. "Even Part." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EvenPart.html

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