A 2009 IEEE Transactions on Computers (TC) guest editorial called computer arithmetic “the mother of all computer research and application topics.” Today, one might question what computer arithmetic still o ers in terms of advancing scienti c research; after all, multiplication and addition haven’t changed. The answer is surprisingly easy: new architectures, processors, problems, application do...

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‎we obtain the asymptotic expansion of the sequence with general term $frac{a_n}{g_n}$‎, ‎where $a_n$ and $g_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎also‎, ‎we obtain some explicit bounds concerning $g_n$ and $frac{a_n}{g_n}$.