about lights

any hints for this...i have a few ideas but they will either TLE or MLE...

Nice task. What's your idea?

[N/p1 + [N/p2] + [N/p3] + ... - [N/LCM(p1, p2)] * 2 - [N/LCM(p1, p3)] * 2 - [N/LCM(p2, p3)] * 2 + ....+ [N/LCM(p1, p2, p3)] * 4 + ......