Harshad Numbers: The Joygiver Digits

We explore Harshad (Niven) numbers—the integers divisible by the sum of their digits. From simple examples like 18 and 1729 to base-dependence, the tiny set of universal Harshads (1, 2, 4, 6), and the intriguing idea of Niven morphic numbers, we uncover the hidden order in digits. We’ll also dive into sharp results—no 21 consecutive Harshads in base 10, the near-universal behavior (almost every number is Harshad or a sum of two Harshads), and the lone exception 11. Along the way, we’ll see why these “joygivers” might be fundamental building blocks in number theory—and what they reveal about the structure of integers.Note:  This podcast was AI-generated, and sometimes AI can make mistakes.  Please double-check any critical information.Sponsored by Embersilk LLC