Help Lakshya!

Lakshya is learning number theory. He reads about the Möbius function : $\mu : \mathbb{N} \longrightarrow \mathbb{Z}$ defined by $\mu(1) = 1$ and

$\large{\mu \left( n \right) =-\sum _{ d|n\\ d\neq n }^{ }{ \mu \left( d \right) } }$

for n>1. However, Lakshya doesn't like negative numbers, so he invents his own function: the Lakshyaous function $\delta : \mathbb{N} \longrightarrow \mathbb{N}$ defined by the relations $\delta (1)=1$ and

$\large{\delta \left( n \right) =\sum _{ d|n\\ d\neq n }^{ }{ \delta \left( d \right) } }$

for n > 1. So he asks his teacher Otto Bretscher to help solve the below question. Otto Bretscher gave him hint but he cannot solve. Help Lakshya determine the value of $1000p+q$ , where $p$ and $q$ are relatively prime positive integers satisfying:

$\large{\frac { p }{ q } =\sum _{ k=0 }^{ \infty }{ \frac { \delta \left( { 15 }^{ k } \right) }{ { 15 }^{ k } } } }$