Properties of terms of OEIS A342810

Abstract

The OEIS sequence A342810 contains the numbers that divide the smallest number that has the sum of their digits. It is proved that if a term $x$ has the form $3^m \times y$ where $m \geq 2$, then all prime factors of $y$ are prime divisors of solutions to $10^n \equiv 1 \; ( \bmod n)$. It is also proved that if a term $x$ has the form $3^m \times p \times q$ where $m \geq 2$, where $p$ is a prime divisor of a solution to $10^n \equiv 1 \; ( \bmod n)$ and where $q$ is the product of all other factors of the prime factorisation of $x$, then all numbers $3^m \times p^i \times q$ are also terms of the sequence A342810 for any integer $i$.