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Corpus ID: 123538236

On the set of divisors of a number

@inproceedings{Bruijn1951OnTS,
title={On the set of divisors of a number},
author={de Ng Dick Bruijn and van C Ebbenhorst Tengbergen and D. Kruyswijk},
year={1951}
}

If z is a natural number and if z=pipfy —Pj is its factorization into primes, then the sum X/ + \2 + '" + \ " will be called the degree of z. Let m be a squarefree natural number of degree /?, i.e., m is the product of n different primes. Let the set of all divisors of m of degree k be denoted by Dk, k = Q, /, •,/?; clearly,the cardinality of Dk is equal to C(n,k), where C(nJ<) denotes the binomial coefficient, n!/[k!(n k)!]. Two natural numbers 5 and f are said to differ in exactly one… Expand

Such entitites are, for example; the divisors of a given integer. It is amusing to observe that the symbol 5: ( N Irepresenting the number of divisors of N containing t prime factors, where n denotes… Expand

Iannucci considered the positive divisors of a natural number $n$ that do not exceed the square root of $n$ and found all numbers whose such divisors are in arithmetic progression. Continuing the… Expand

Let n be an integer with n ≥ 2. A set A ⊆ ℝ n is called an antichain (resp. weak antichain) if it does not contain two distinct elements x = ( x 1 , …, x n ) and y = ( y 1 , …, y n ) satisfying x i ≤… Expand