I am lookin for an app (iOS or Android) that turns any smartphone into a wireless microphone for any kind of event. For example I can talk in my phone and sound is broadcasted in real time to the speakers. I don’t want to buy dozens of mics.
Don't, just don't. Using smartphones as microphones for live sound is really highly ill-advised. You will have all kinds of network latency issues, feedback issues (as they are generally designed to be omni-directional), quality issues, etc. You can do it in a pinch for a recording maybe, but if you are using it for reinforcement, you are majorly asking for trouble.
If you really, really want to continue down that path, any voice chat client will do what you are looking for. Just setup one device on the call to be plugged in to the sound board and it will play the audio through the PA, but don't be surprised when you have major issues.
If I absolutely had to do something like this, I'd probably use something like TeamSpeak 3 which is designed for multi-person voice communications. It has a mobile client and allows for a lot of control over volumes of individual speakers and can even enable certain speakers to automatically make other speakers more quiet. It is free for non-profit use (up to 512 users) or can be licensed for more than that. Alternately, Mumble could be used for free, but the platform itself isn't quite as flushed out as TeamSpeak. Again though, I can't emphasis enough how much I would advise against this.
As an experiment, use skype or hangout because everybody has it installed already, and you can hook it into the PA with some real soundcard. If you want to go further, use some sound server as Jack on iOs with seperate recording app and streaming app. That would be the only way around the noise reduction and echo cancellation algorithms mandatory in telephony applications. The sound of the mic will alwys be horrific compared to a >50$ PA mic.