Permutation-Invariant Niven Numbers

This paper introduces permutation-invariant Niven numbers (PINNs), a novel class of Niven numbers where all digit permutations (with leading zeros automatically ignored) must retain the Niven property. We demonstrate that there exist infinitely many such numbers and that their magnitude is unbounded. Furthermore, we present an exhaustive search method for identifying permutation-invariant Niven numbers. Complete classifications for digit lengths up to 9 are provided, and an infinite family for arbitrary digit lengths is constructed. The asymptotic density of PINNs is shown to be zero, and various arithmetic and combinatorial properties are investigated. We present a novel parameterization of infinitely many repdigit PINNs through Conjecture 1, which establishes an explicit multiplicative structure involving distinguished prime factors derived from repunit arithmetic. This provides a systematic method for generating infinitely many new repdigit Niven numbers.