MathDB

Call a function

\mathbb Z_{>0}\rightarrow \mathbb Z_{>0}

\emph{M-rugged} if it is unbounded and satisfies the following two conditions:

(1)

f(n)|f(m)

and

f(n)<f(m)

then

n|m

(2)

|f(n+1)-f(n)|\leq M

. a. Find all

1-rugged

functions. b. Determine if the number of

2-rugged

functions is smaller than

2019

P4