An integer is k-smooth if it has no prime factors >k. The following table gives the first few k-smooth numbers for small k. Berndt called the 7-smooth numbers "highly composite numbers." k | OEIS | k-smooth numbers 2 | A000079 | 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ... 3 | A003586 | 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, ... 5 | A051037 | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, ... 7 | A002473 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, ... 11 | A051038 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, ...

highly composite number | rough number | round number | semiprime