There is a question whether we count the Birchos Hatorah as three brachos or two brachos. The general minhag is two and therefore we say והערב נא with a vov, as a continuation of the first brachah. According to this, one should not answer amen after the first brachah, and in order to avoid this, the one reciting the brachah should say the words לעסוק בדברי תורה silently. Similarly, even in a situation where one is saying the bracha out loud for the listener to hear and thereby fulfil his obligation, the listener should not respond amen after the words לעסוק בדברי תורה.