18.781 (Spring 2016): Floor and arithmetic functions
نویسنده
چکیده
2. Arithmetic functions 19 2.1. Arithmetic functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2. Multiplicative functions . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3. The Dirichlet convolution . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4. Examples of Dirichlet convolutions . . . . . . . . . . . . . . . . . . . 34 2.5. Möbius inversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6. Dirichlet convolution and multiplicativity . . . . . . . . . . . . . . . 43 2.7. Explicit formulas from multiplicativity . . . . . . . . . . . . . . . . 48
منابع مشابه
A remark on the means of the number of divisors
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 $frac{A_n}{G_n}$.
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