Add to ORKGABSTRACT: For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power part of n respectively. That is, a(n) denotes the largest k-th power less than or equal to n, and b(n) denotes the smallest k-th power greater than or equal to n. In this paper, we study the properties of the sequences {a(n)} and {b{n)}, and give two interesting asymptotic formulas. Xey words and phrases: Inferior and superior k-th power part; Mean value; Asymptotic formula. 1
Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bri...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractWe obtain, for quadratic and cyclotimic fields, asymptotic formulas for two arithmetic funct...
For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power part of n ...
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Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main pur...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
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Abstract For any positive integer n, the Smarandache power function SP (n) is defined as the smalles...
AbstractK. Thanigasalam has shown that for any positive integer k the sequence of positive integers ...
We improve a result of Bennett concerning certain sequences involving sums of powers of positive in...
Abstract Let q ≥ 3 be a fixed positive integer, eq(n) denotes the largest exponent of power q which ...
Let T(n) denote the product of divisors of the positive integer n. We introduce and study some basic...
Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bri...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractWe obtain, for quadratic and cyclotimic fields, asymptotic formulas for two arithmetic funct...
For any positive integer n, let a{n) and b{n) denote the inferior and superior k-th power part of n ...
ABSTRACT. Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factoriz...
Let n be any positive integer, Pd(n) denotes the product of all positive divisors of n. The main pur...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
Abstract For any positive integer n, we define the arithmetical function G(n) as G(1) = 0. If n>...
Abstract For any positive integer n, the Smarandache Superior Prime Part Pp(n) is the smallest prime...
Keywords: The main purpose of this paper is using the elementary method to study the asymptotic prop...
Abstract For any positive integer n, the Smarandache power function SP (n) is defined as the smalles...
AbstractK. Thanigasalam has shown that for any positive integer k the sequence of positive integers ...
We improve a result of Bennett concerning certain sequences involving sums of powers of positive in...
Abstract Let q ≥ 3 be a fixed positive integer, eq(n) denotes the largest exponent of power q which ...
Let T(n) denote the product of divisors of the positive integer n. We introduce and study some basic...
Asymptotic formulas for the positive moments of rank and crank of partitions were obtained by K. Bri...
For a positive integer n we let τ(n) denote the number of its positive divisors. In this paper, we o...
AbstractWe obtain, for quadratic and cyclotimic fields, asymptotic formulas for two arithmetic funct...