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We show that for each $j$ and each prime $p$, if $p\\leq2^{j-1}$ then $p$ divides $c_{j}$. Consequently, $$\\ln c_{j}>\\frac{1}{4}\\cdot2^{j}\\,\\,\\mathrm{for}\\,j\\geq5$$ If we also have $p\\equiv3\\,(\\mathrm{mod\\,4)}$ then $p^{2^{j-\\left\\lceil \\lg p\\right\\rceil }}$ divides $c_{j}$. 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