For a positive integer n, let g(n) be the largest divisor of n not exceeding the square root of n (OEIS A033676), and group the integers into entry layers G_a = {n : g(n) = a}. Each layer splits into an infinite "prime spine" together with a finite set of composite multipliers X_a = {m composite : a <= m <= a^2 and g(a*m) = a}, the rows of OEIS A163925, whose sizes form OEIS A163926. For prime a the size satisfies |X_a| ~ a^2 / (2 log^2 a). This paper treats prime-power layers a = p^k and shows that the size exponent decreases with the multiplicity k. Two elementary structural results valid for all a are established: a smallest-prime-factor floor, and a cofactor squeeze m / P-(m) <= a, where P-(m) is the smallest prime factor of m. Applying these to the pair of divisors p^i * P-(m) and p^j * (m / P-(m)) yields a multiplicity inequality i + j >= k + 1, which confines every member coprime to p to the band m <= a^(1 + 1/k). Combined with a rough-number sieve estimate and an explicit lower-bound family, this gives, for fixed k and p >= 3, that |X_(p^k)| is of order a^(1 + 1/k) / log^2 a (with a = p^k): an exponent ladder 1 + 1/k graded by the multiplicity of the layer index, which recovers the prime case a^2 / log^2 a at k = 1. The argument is elementary throughout, using only the prime number theorem, Mertens' theorem, and the sieve fundamental lemma. Numerical evidence through k = 4 is included.