Highly composite number
= Highly composite number
{title2=$\tau(n)>\max_{1\leq m<n}\tau(m)$}
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.