Hexagonal numbers are given by \(H_k = k(2k-1)\) for \(k \geq 1\). First terms: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276.
A defining property: every hexagonal number is also triangular — specifically, \(H_k = T_{2k-1}\). So 6 = T_3, 15 = T_5, 28 = T_7, 45 = T_9, etc.
Notably, 28 — the second perfect number — is also a hexagonal number, and several other perfect numbers (496, 8128) are hexagonal too. In fact, every even perfect number is hexagonal.