From Tufts website:
"Writings that urged young men to study philosophy formed a distinct literary genre among the ancients under the name “protreptics.” The Epistle to Menoeceus of Epicurus is an extant example."
And this article: "Ancient Philosophic Protreptic and the Problem of Persuasive Genres"
https://www.jstor.org/stable/10.1525/rh.1986.4.4.309
Quote"The protereptic has as its explicit aim the winning of a student for philosophy. The student must be won at different levels--for the love of wisdom generally, for the choice of a particular school, for full commitment to the rigors of an advanced discipline."