Largest power of 2 that divides \$n\$
Python 2, 13 bytes
Takes a positive integer \$ n \$ as input and returns the \$ n \$th term of the sequence.

lambda n:n&amp;-n

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The largest power of \$ 2 \$ that divides \$ n \$ is also the lowest set bit. The bitwise magic is a bit difficult to explain, but it uses the fact that ~n + 1 in its binary representation produces the same lowest set bit as n.
Python 2, 26 bytes
Outputs the sequence infinitely.

n=1
while 1:print-n&amp;n;n+=1

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Python 2, 33 bytes
Takes a positive integer \$ n \$ as input and returns the first \$ n \$ terms of the sequence.

f=lambda n:n*[0]and f(n-1)+[n&amp;-n]

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