Denominator Profiles and Prime-Power Thresholds in Binomial Coefficients

We study the reduced denominators of $\binom{n}{k}/n$ and their least common multiples over restricted sets of lower indices. A prime-power witness argument gives exact formulas for every cutoff $K$ under both coprimality and nonmultiple restrictions, and more generally for suitable saturated sets of indices. These formulas determine the least cutoff for the five prime-indexed families OEIS A343249–A343253 and characterize all successful cutoffs for arbitrary integer bases. We derive the composite-base transition threshold described in the Comments of A345531 and the admissible-set assertions of de Castro (2022). Two further applications address the odd values in A056606 and the denominator divisibilities associated with A347563 and A213999, using established identities for binomial-row least common multiples and a harmonic-number formula. The arguments are valid for all stated indices; exact computations are presented separately as illustrations and consistency checks.