Overview of the modifications to the HMF due to the PBH contribution to the power spectrum. The Sheth & Tormen (2002) HMF (n) at z = 11 is plotted as a function of halo mass (M_h) for a pure ΛCDM cosmology and for PBHs with lognormal mass functions, constituting a fraction f_PBH = 10⁻⁵ of the total dark matter density; each color corresponds to a different PBH mass M_PBH = 10⁹ M_⊙, 10¹¹ M_⊙, whereas continuous (dashed) lines represent monochromatic (lognormal with σ = 0.5) mass functions. For reference, we show the corresponding power spectra at z = 0 (P_CDM, Eq. 1) as a function of the wavenumber (k) as an inset.