Is it permissible to remain with irreligious friends who do not pray and listen to music, with the intention of inviting them [to Islam], while fearing their negative influence?

Associating with wicked people is forbidden by Islamic law if you fear being influenced by them, due to the hadiths that warn against bad companions, such as the Prophet's saying, "Do not accompany anyone but a believer," and his saying, "The example of a good companion and a bad companion is like the bearer of musk and the blower of bellows." Thus, averting the harm of being influenced by them takes precedence over gaining the benefit of inviting them to Islam. However, if it is possible to invite them through communication means without direct mingling, then that is good, as it combines preserving one's religion with inviting to Allah.