On the Number of Divisors of Binomial Coefficients

This paper deals with the problems of the upper and lower orders of growth of the ratios of the divisor functions of “adjacent” binomial coefficients, i.e., of the numbers of combinations of the form $C_{n}^{k}$ and $C_{n}^{k+1}$ or $C_{n}^{k}$ and $C_{n+1}^{k}$. The suprema and infima of the corresponding ratios are obtained.