Let be the divisors of positive integer (including 1 and )

MATHEMATICS · Single correct · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Let

x_1, x_2, x_3, \dots, x_k

be the divisors of positive integer

n

(including 1 and

n

). If

x_1 + x_2 + x_3 + \dots + x_k = 75

. Then

\sum_{i=1}^{k} \left(\frac{1}{x_i}\right)

is equal to : (a)

\frac{75}{k}

(b)

\frac{75}{n}

(c)

\frac{1}{n}

(d)

\frac{1}{75}