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On the Natural Density of the Niven Numbers
Some examples of Niven numbers are 8, 12, 180, and 4050. The set of Niven numbers is infinite since any positive integral power of 10 is a Niven number. Even though a variety of ideas, results andExpand
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A PARTIAL ASYMPTOTIC FORMULA FOR THE NIVEN NUMBERS
A Niven number is a positive integer that is divisible by its digital sum. That is, if n is an integer and s(n) denotes the digital sum of n, then n is a Niven number if and only if sin) is a factorExpand
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Chebyshev's inequality and natural density
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ON AN ASYMPTOTIC FORMULA FOR THE NIVEN NUMBERS
A Niven number is a positive integer which is divisible by its digital sum. A discussion of the possibility of an asymptotic formula for N(x) is given. Here, N(x) denotes the nmber of Niven numbersExpand
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ON CONSECUTIVE NIVEN NUMBERS
INTRODUCTION In [1] the concept of a Niven number was introduced with the following definition. Definition: A positive integer is called a Niven number if it is divisible by its digital sum. VariousExpand
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An extension of a theorem by Cheo and Yien concerning digital sums
For a nonnegative integer k, let s(k) denote the digital sum of k. In [1], Cheo and Yien prove that, for a nonnegative integer x, x 1 (1.1) £ s(k) = (4.5)a: log x + 0(x) . fc=o Here 0(f(x)) is theExpand
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High order stiffly stable linear multistep methods
Stiffly stable linear k-step methods of order k for the initial-value problem are studied. Examples for k = 1, 2, and 3 were discovered by use of Adams-type methods. A large family of stiffly stableExpand
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Tau numbers, natural density, and Hardy and Wright's theorem 437
An element of the set T= {n:τ(n) is a factor of n} is called a Tau number, where τ(n) denotes the number of divisors of the integer n. We determine the natural density of this set by use of Hardy andExpand
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