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An inequality involving integer partitions

For integers $n\ge k\ge0$, let $p(n,k)$ denote the number of ways to write $n$ as a sum of $k$ positive integers (repetition allowed). For example, $p(6,3)=3$ since $$6=1+1+4=1+2+3=2+2+2.$$ QUESTION. ...
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upper and lower bounds on rowlands sequence

rowlands sequence is defined as follows \begin{equation} a_{n}=a_{n-1} + b_{n} \end{equation} where $b_{n} = gcd(a_{n-1}, n)$ for $n>h$ it originates from E. Rowlands 2008 paper "A Natural ...
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