Answer by John Omielan for How to prove formula related to $2$-adic valuation...
Your proposed formula is always true. To show this, first to reduce the algebra involved, define$$m = \lfloor \log_2 n \rfloor, \; \; j = \nu_2(n) \tag{1}\label{eq1A}$$Since $m$ is the index of the...
View ArticleHow to prove formula related to $2$-adic valuation / $2$-adic absolute value...
I would like to prove the following formula, which I have verified for every positive integer $n \ge 1$ up to $n = 10000$:$$n - \sum_{k=0}^{\lfloor \log_2{n}...
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