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On the Number of Binomial Coefficients which are Divisible by their Row Number

Published online by Cambridge University Press:  20 November 2018

Neville Robbins
Neville Robbins*
Affiliation:
California State College, San Bernardino, CA 92407
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Abstract

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If n is a natural number, let A(n) be the number of integers, k, such that 0 < k < n and n divides . Then ϕ(n) ≤ A(n) ≤ n - 1 - 2ω(n) + ɛ, where ?(n) denotes the number of distinct prime factors of n, and ɛ = 0 unless n is twice a prime, in which case ɛ = 1.

Keywords

10A99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 3 , 01 September 1982 , pp. 363 - 365
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Carlitz, L., The number of binomial coefficients divisible by a fixed power of a prime. Rend. Circ. Mat. Palermo (2) 16 (1967), 299-320.Google Scholar
2. Harborth, H., Divisibility of binomial coefficients by their row number. Am. Math. Monthly 84 (1977), 35-37.Google Scholar