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Jordan’s arithmetical function
 Gazeta Matematică Seria B
"... In the recent book [1] there appf'ar certain arithmetic functions which are similar to the Smarandache function. In a rf'("ent paper [2} we have considered certain generalization or duals of the Smarandache fnnct:ion 8(11). In this note we wish to point out that the arithmetic functio ..."
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In the recent book [1] there appf'ar certain arithmetic functions which are similar to the Smarandache function. In a rf'("ent paper [2} we have considered certain generalization or duals of the Smarandache fnnct:ion 8(11). In this note we wish to point out that the arithmetic functions introciu(wl in [I] all are particular cases of our function Fj, defined in the following manner (sPt> [2J or [3]). Let f: N' "r N * be an arithmetical function which satisfies the following property: (Pd For each n E N " there exists at lea.'5t a k E N * such that nlf(k). Let FJ: N' "r N * defined by FJ(n) = miu{k E N * ; n/f(k)} (1) In Problem 6 of [1 J it is defined the " ceil fuuction of tth order " by St ( n) = min { k: nJe}. Clearly here one can selpct f(m) = mt (m = 1,2,...), where t 2: 1 is fixed. Property (Pr) is satisfied wit.h k = nt. For fern) = m(m + 1), one obtains the "Pseudo2 Smarandache " function of Problem i. The Smarandache "doublefactorial " function where SDF(n) = miu{k: nlk!!} I, 3.!)... k if I.: is odd
A generalization of the Smarandache function
 Scientia Magna
"... Abstract For any positive integer n, we define the function P (n) as the smallest prime p such that n  p!. That is, P (n) = min{p: n p!, where p be a prime}. This function is a generalization of the famous Smarandache function S(n). The main purpose of this paper is using the elementary and analy ..."
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Abstract For any positive integer n, we define the function P (n) as the smallest prime p such that n  p!. That is, P (n) = min{p: n p!, where p be a prime}. This function is a generalization of the famous Smarandache function S(n). The main purpose of this paper is using the elementary and analytic methods to study the mean value properties of P (n), and give two interesting mean value formulas for it.
Northwest University
"... Papers in electronic form are accepted. They can be emailed in Microsoft ..."
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Papers in electronic form are accepted. They can be emailed in Microsoft
This book can be ordered in microfilm format from: Books on Demand
, 2002
"... AB/AC=(MB/MC)(sin u / sin v) ..."
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Books on Demand ProQuest Information and Learning
"... AB/AC=(MB/MC)(sin u / sin v) ..."
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A NOTE ON EXPONENTIAL DIVISORS AND RELATED ARITHMETIC FUNCTIONS
"... Let n> 1 be a positive integer, and n = pα11 · · · pαrr its prime factorization. A number d  n is called an Exponential divisor (or edivisor, for short) of n if d = pb11 · · · pbrr with bi  ai(i = 1, r). This notion has been introduced by E.G. Straus and M.V. Subbarao[1]. Let σe(n), resp. ..."
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Let n> 1 be a positive integer, and n = pα11 · · · pαrr its prime factorization. A number d  n is called an Exponential divisor (or edivisor, for short) of n if d = pb11 · · · pbrr with bi  ai(i = 1, r). This notion has been introduced by E.G. Straus and M.V. Subbarao[1]. Let σe(n), resp. de(n) denote the sum,
MEAN VALUE OF THE ADDITIVE ANALOGUE OF SMARANDACHE FUNCTION ∗
"... Abstract For any positive integer n, let S(n) denotes the Smarandache function, then S(n) is defined the smallest m ∈ N+, where nm!. In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it. ..."
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Abstract For any positive integer n, let S(n) denotes the Smarandache function, then S(n) is defined the smallest m ∈ N+, where nm!. In this paper, we study the mean value properties of the additive analogue of S(n), and give an interesting mean value formula for it.
MEAN VALUE OF THE ADDITIVE ANALOGUE OF SMARANDACHE FUNCTION
"... Abstract For any positive integer n, let Sdf(n) denotes the Smarandance double factorial function, then Sdf(n) is defined as least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of the additive analogue of Sdf(n) and give an interesting mean val ..."
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Abstract For any positive integer n, let Sdf(n) denotes the Smarandance double factorial function, then Sdf(n) is defined as least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of the additive analogue of Sdf(n) and give an interesting mean value formula for it.
ON THE MEAN VALUE OF THE SMARANDACHE DOUBLE FACTORIAL FUNCTION
"... Abstract For any positive integer n, the Smarandache double factorial function Sdf(n) is defined as the least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of Sdf(n), and give an interesting mean value formula for it. ..."
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Abstract For any positive integer n, the Smarandache double factorial function Sdf(n) is defined as the least positive integer m such that m!! is divisible by n. In this paper, we study the mean value properties of Sdf(n), and give an interesting mean value formula for it.
A note on fminimum functions
"... Abstract For a given arithmetical function f: N → N, let F: N → N be defined by F (n) = min{m ≥ 1: nf(m)}, if this exists. Such functions, introduced in [4], will be called as the fminimum functions. If f satisfies the property a ≤ b = ⇒ f(a)f(b), we shall prove that F (ab) = max{F (a), F (b)} ..."
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Abstract For a given arithmetical function f: N → N, let F: N → N be defined by F (n) = min{m ≥ 1: nf(m)}, if this exists. Such functions, introduced in [4], will be called as the fminimum functions. If f satisfies the property a ≤ b = ⇒ f(a)f(b), we shall prove that F (ab) = max{F (a), F (b)} for (a, b) = 1. For a more restrictive class of functions, we will determine F (n) where n is an even perfect number. These results are generalizations of theorems from [10], [1], [3], [6].