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On the Distance Between Consecutive Divisors of an Integer
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- Journal:
- Canadian Mathematical Bulletin / Volume 29 / Issue 2 / 01 June 1986
- Published online by Cambridge University Press:
- 20 November 2018, pp. 208-217
- Print publication:
- 01 June 1986
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- Article
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Let ω(n) denote the number of distinct prime divisors of a positive integer n. Then we define
and 
where 
are primes and r ≥ 2. Similarly denote by 
the number of divisors of n and let 
be defined by 
where 
are the divisors of n. We prove that there exists constants A and B such that 
and 
and 
where 
are primes and 
the number of divisors of 
be defined by 
where 
are the divisors of 
and 
