This is a late addition but I was looking for information on the scale function myself and though it might help somebody else as well.
To modify the response from Ricardo Saporta a little bit.
Scaling is not done using standard deviation, at least not in version 3.6.1 of R, I base this on "Becker, R. (2018). The new S language. CRC Press." and my own experimentation.
X.man.scaled <- X/sqrt(sum(X^2)/(length(X)-1))
X.aut.scaled <- scale(X, center = F)
The result of these rows are exactly the same, I show it without centering because of simplicity.
I would respond in a comment but did not have enough reputation.