Corrections to Hardy–Ramanujan's 1918 Partition Formula

This note identifies four sign discrepancies in the partition multipliers tabulated by Hardy and Ramanujan in 1918, at (h,k) = (1,15), (14,15), (3,16), and (13,16). It derives the corresponding corrections to A15(n) and A16(n), including the zero-residue classes. Exact verification using the Selberg–Whiteman representation and cyclotomic identities for residues modulo 15 and 16 accompanies the manuscript.