Exact prime-power block counts for isosceles MacMahon numbers

For every prime p and integer e >= 1, we count exactly the positive parameter pairs 1 <= k,m < p^e for which the isosceles MacMahon number M(k,m,m) is not divisible by p. We obtain a closed expression for odd primes and the formula (e-1)2^(e-1) for p=2. The resulting counts give the growth order on general square blocks and zero two-dimensional density. Through the Li-Zanello criterion, they also enumerate weak Lefschetz parameters in the stated family of monomial complete intersections.