 Highly composite number

A positive integer whose divisor count strictly exceeds that of every smaller positive integer. A record scan maintains the largest earlier value of the divisor function and emits exactly candidates exceeding it. Equality does not create a new record; the first candidate is handled by a zero initial record.

A highly composite number is a positive integer that has more divisors than any smaller positive integer. In other words, it is a number that has a greater number of divisors than all the integers less than it. The concept of highly composite numbers was introduced by the mathematician Srinivasa Ramanujan.