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Inspired by the question of Graeme L. Cohen and Herman J. J. te Riele , TheAuthors of \cite{Graeme L} who they investigated a question Given $n$ is therean integer $k$ for which $\sigma^k(n) = 0 \bmod n$? They did this in a $1995$paper and asserted through computation that the answer was yes for $n \leq400$,The aim of this paper is to give a negative answer to the reverse questionof Graeme L. Cohen and Herman J. J. te Riele such that we shall prove thatthere is no fixed integer $n $ for which $\sigma^k(n) = 0 \bmod n$ for alliteration $k$ of sum divisor function using H.Lenstra problem for aliquotsequence at the same time we prove that there exist an integer $n$ satisfies$\sigma^k(n) = 0 \bmod n$ for all odd iteration $k$ rather than that we shallprove that if $n$ is multiperfect with $L$ the lcm (the least common multiple )of $1$+each exponents in the prime factorization of $n$ , and with $L$ prime,then $n=6$.we conclude our paper with open conjecture after attempting to showthat $6$ is the only integer satisfy periodicity with small period dividing $L$

On congruence of the iterated form $\sigma^k(m) = 0 \bmod m$