2021/06/09 by Rüdiger Jehn, Jehn, Rüdiger, Kester Habermann +1
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM
paper · pdf · doi:10.48550/arxiv.2106.05866
6 pages
arxiv created 2021/06/09 · arxiv updated 2021/06/11
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 3m × y where m ≥ 2, then all prime factors of y are prime divisors of solutions to 10n ≡ 1 ( \bmod n). It is also proved that if a term x has the form 3m × p × q where m ≥ 2, where p is a prime divisor of a solution to 10n ≡ 1 ( \bmod n) and where q is the product of all other factors of the prime factorisation of x, then all numbers 3m × pi × q are also terms of the sequence A342810 for any integer i.