Find all $a$, so $q$ prime number which ,$q\times n= aaaaaaa$

Question

I need your helping to find all the $a$ numbers,which follow the next rules:

there is prime number $ 2\lt n\in \mathbb N$ and $ 5\neq q\in \mathbb N$ so that the digits of $n\times q$ are only $a$.

for example:$n\times q=aaaaaaa$

if $n=7$,$a=1, 7\times 15873=111111$

and also if $2\lt n\in \mathbb N$ is odd and not divided by $5$, $q\in \mathbb N$* , so $n\times q$ are only $a$ digits.

I need to find all the $a$ numbers which follow this rule , except $1$.

Answer 1

All numbers from $a = 1...9$ follow the rule.

$7\times 15873=111111$

$7\times 2*15873=222222$

$7\times 3*15873=333333$

$7\times 4*15873=444444$

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