The amount of power you need depends a lot on situation, in the OPs game there isn't really a need for a military at all, except for garrisons as both neighbours could easily be brought to friendly by adopting religion. Obviously if you have warmongers near that you can't control then your going to want enough troops to fend them off, or preferably to wipe them out before they get any ideas.
The power ratio itself tends to give overestimates of how strong AIs actually are as a considerable bulk of their power is always tied up in defensive units and city garrisons. Combined with AI weakness at war this means defending against an AI attacker is very doable with far less power than they have.
While learning noble as long as you keep about even with your neighbours power then you should easily have enough to fend off any invasion, though you may want to rebalance your unit building to have fewer spears and archers with more axes and swords. You also don't need 3+ troops in every city, cities behind your front line have a very low risk of being attacked, so low that I often leave nothin but warriors 'defending' many core cities, sometimes as late as the modern era.
The source of the 1.6 is from someone who did some code diving a few years ago, during one of these how much is enough discussions. He reported that the AIs were coded to not consider attacking anyone with a ratio of 1.6 or higher, no matter what the diplo or other considerations. So, that doesn't mean get a ratio of 1.6.
The only related thread I remember was the "any logic in AI DOWs" thread, where DanF stated that to prevent Monty from attacking you you actually needed 1.95 times his power!
From that same thread also came that if you don't exceed the AIs no war threshold, then it doesn't matter if your powers 1.5 times or 0.3 times theirs in their decision to attack.
That thread highlighted that diplomacy was the way to peace, sinking the myth of peace through power being a good plan.