# Help Lakshya!

Lakshya is learning number theory. He reads about the Mobius function : $$\mu : \mathbb{N} \longrightarrow \mathbb{Z}$$ defi ned 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:

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

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