Composite Numbers Map for the OEIS

(Internal code: C003595) This preprint presents a reference map of composite-number classes and their representation in the On-Line Encyclopedia of Integer Sequences (OEIS). Its purpose is to bring together, within a single factorization-based framework, sequences that are otherwise distributed across many separate OEIS entries. Composite integers are organized into the three principal FTC classes—prime-power, squarefree, and mixed composites—and into several derived subclasses, including semiprimes, sphenic numbers, powerful and weak mixed composites, minimal mixed composites, higher-order minimal mixed composites, and nonminimal mixed composites. For each class, the map records the corresponding OEIS identifiers, complement relations, disjoint-union or intersection decompositions, odd and even subdivisions, arithmetic definitions, and equivalent descriptions in terms of A001221(n) = omega(n), the number of distinct prime factors of n, and A001222(n)=Omega(n), the number of prime factors of n counted with multiplicity. The current version expands the parity structure of the mixed composite class. It records the odd and even components of powerful and weak mixed composites, minimal and nonminimal mixed composites, and higher-order minimal mixed composites. The even higher-order minimal mixed composites are further divided according as 2 or an odd prime is the unique prime occurring with exponent 2. Subclasses that do not yet have independent OEIS entries are recorded under the internal identifiers C003636-C003645. These refinements provide a systematic way to identify unrepresented or partially represented cells of the map. Existing OEIS sequences are recognized as occupied cells, while natural subclasses without separate entries are retained as candidate sequences for further study and possible submission. The map also connects these arithmetic classifications with the geometry of the Triangular Multiplication Table (TMT). In the sharp admissible range 1