MathDB

Let

x

be a natural number. We call

\{x_0,x_1,\dots ,x_l\}

a factor link of

x

if the sequence

\{x_0,x_1,\dots ,x_l\}

satisfies the following conditions: (1)

x_0=1, x_l=x

; (2)

x_{i-1}<x_i, x_{i-1}|x_i, i=1,2,\dots,l

. Meanwhile, we define

l

as the length of the factor link

\{x_0,x_1,\dots ,x_l\}

. Denote by

L(x)

and

R(x)

the length and the number of the longest factor link of

x

respectively. For

x=5^k\times 31^m\times 1990^n

, where

k,m,n

are natural numbers, find the value of

L(x)

and

R(x)

Problem Statement