Great article, @William, thanks for sharing! For those into technical details details and history, check out Stephen Wolfram's notes on number-theoretic sequences from "A New Kind of Science" book:
https://www.wolframscience.com/nks/notes-4-4--properties-of-number-theoretic-sequences
https://www.wolframscience.com/nks/notes-4-4--iterated-aliquot-sums
