No, I'm not positing dependence or anything like that. But I think that when similar sounding sorts of things occur in contemporary literature, examining both occurrences can aid our understanding of what is being discussed. Thus, when the similarities are between the New Testament and the Apostolic Fathers, our understanding of the NT may be aided by further examining the AF instance. I think too often people notice similarities and end up going down the quotation/allusion/echo rabbit trail to little or no profit.

So, I noticed the following awhile back. First is from the New Testament, 1Ti 1.3-7, pay particular attention to verses 6 and 7, and the description of the teachers in each example. Is our understanding of the portrayal of false teachers enhanced? Not that I'm saying the stuff in Hermas is transferable to the portrayal in First Timothy; I'm just looking at the idea of false teachers and how they are portrayed by those who think they are the true teachers.

With that said, here we go.

3 Καθὼς παρεκάλεσά σε προσμεῖναι ἐν Ἐφέσῳ πορευόμενος εἰς Μακεδονίαν, ἵνα παραγγείλῃς τισὶν μὴ ἑτεροδιδασκαλεῖν 4 μηδὲ προσέχειν μύθοις καὶ γενεαλογίαις ἀπεράντοις, αἵτινες ἐκζητήσεις παρέχουσιν μᾶλλον ἢ οἰκονομίαν θεοῦ τὴν ἐν πίστει. 5 τὸ δὲ τέλος τῆς παραγγελίας ἐστὶν ἀγάπη ἐκ καθαρᾶς καρδίας καὶ συνειδήσεως ἀγαθῆς καὶ πίστεως ἀνυποκρίτου, 6 ὧν τινες ἀστοχήσαντες ἐξετράπησαν εἰς ματαιολογίαν 7 θέλοντες εἶναι νομοδιδάσκαλοι, μὴ νοοῦντες μήτε ἃ λέγουσιν μήτε περὶ τίνων διαβεβαιοῦνται. (1Ti 1.3-7, NA27)

3 As I urged you while I was on my way to Macedonia, remain at Ephesus so that you may instruct certain people not to teach contrary doctrine, 4 nor to cling to myths and endless genealogies—which give rise to useless speculations rather than administration from God that is by faith. 5 The goal of our instruction is love from a pure heart and a good conscience and faith unfeigned. 6 Some, having gone astray from these, have turned away into empty talk, 7 desiring to be teachers of the law, not understanding either what they are saying or the matters about which they themselves make confident assertions. (1Ti 1.3-7, my own translation)

Now, here's Hermas Similitudes IX xxii.1-4 (99.1-4) in Holmes' edition:

99.1 Ἐκ δὲ τοῦ ὄρους τοῦ πέμπτου τοῦ ἔχοντος βοτάνας χλωρὰς καὶ τραχέος ὄντος οἱ πιστεύσαντες τοιοῦτοί εἰσι· πιστοὶ μέν, δυσμαθεῖς δὲ καὶ αὐθάδεις καὶ ἑαυτοῖς ἀρέσκοντες, θέλοντες πάντα γινώσκειν, καὶ οὐδὲν ὅλως γινώσκουσι. (2) διὰ τὴν αὐθάδειαν αὐτῶν ταύτην ἀπέστη ἀπʼ αὐτῶν ἡ σύνεσις καὶ εἰσῆλθεν εἰς αὐτοὺς ἀφροσύνη μωρά. ἐπαινοῦσι δὲ ἑαυτοὺς ὡς σύνεσιν ἔχοντας καὶ θέλουσιν ἐθελοδιδάσκαλοι εἶναι, ἄφρονες ὄντες. (3) διὰ ταύτην οὖν τὴν ὑψηλοφροσύνην πολλοὶ ἐκενώθησαν ὑψοῦντες ἑαυτούς· μέγα γὰρ δαιμόνιόν ἐστιν ἡ αὐθάδεια καὶ ἡ κενὴ πεποίθησις· ἐκ τούτων οὖν πολλοὶ ἀπεβλήθησαν, τινὲς δὲ μετενόησαν καὶ ἐπίστευσαν καὶ ὑπέταξαν ἑαυτοὺς τοῖς ἔχουσι σύνεσιν, γνόντες τὴν ἑαυτῶν ἀφροσύνην. (4) καὶ τοῖς λοιποῖς δὲ τοῖς τοιούτοις κεῖται μετάνοια· οὐκ ἐγένοντο γὰρ πονηροί, μᾶλλον δὲ μωροὶ καὶ ἀσύνετοι. οὗτοι οὖν ἐὰν μετανοήσωσι, ζήσονται τῷ θεῷ· ἐὰν δὲ μὴ μετανοήσωσι, κατοικήσουσι μετὰ τῶν γυναικῶν τῶν πονηρευομένων εἰς αὐτούς.
Holmes, M. W. (1999). The Apostolic Fathers : Greek texts and English translations (Updated ed.) (504). Grand Rapids, Mich.: Baker Books.

99. “And from the fifth mountain, the rugged one with the green grass, are believers such as these: they are faithful, but slow to learn, arrogant, and self-satisfied; though they want to know everything, they know nothing at all. (2) Because of this arrogance of theirs, understanding has left them and a foolish stupidity has taken possession of them. Yet they praise themselves for having wisdom and want to be volunteer teachers, foolish though they are. (3) So, because of this pride many people, while attempting to exalt themselves, have been ruined, for arrogance and overconfidence are a mighty demon. Many of these, therefore, were rejected, but some, comprehending their own foolishness, repented and believed, and submitted themselves to those with understanding. (4) And of the rest of these people repentance remains a possibility, for they were not really evil but rather stupid and short on understanding. So these will, if they repent, live for God, but if they do not repent they will dwell with the women who do harm to them.”
Holmes, M. W. (1999). The Apostolic Fathers : Greek texts and English translations (Updated ed.) (505). Grand Rapids, Mich.: Baker Books.