The minimal number with a given number of divisors
نویسندگان
چکیده
منابع مشابه
The minimal number with a given number of divisors
A number n is said to be ordinary if the smallest number with exactly n divisors is p q1−1 1 · · · p qa−1 a where q1 · · · qa is the prime factorization of n and q1 ≥ . . . ≥ qa (and where pk denotes the k-th prime). We show here that all square–free numbers are ordinary and that the set of ordinary numbers has natural density one.
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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 $frac{A_n}{G_n}$.
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متن کاملa 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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2006
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2005.04.004