4 problems

Let $\mathbb K=\{k_i\}_{i\in\mathbb N}$ be the set of integers produced by the paper's iterative construction, and let … be the set of square-free, or Möbius, numbers. Auil's enume…

Miller et al.'s conjecture. There exists an infinite sequence of square-free integers

Fix a base $b\geq 2$ and let $\overleftarrow{n}$ denote the integer obtained by reversing the base-$b$ digits of $n$. A square-free palindrome is a positive integer that is square-…

Let $v(n)$ denote the sum of the primes and exponents appearing in the prime factorization of $n$, and let $r_{10}(n)$ be the digit reversal of $n$ in base ten. A $v$-palindrome in…