powering arduino with a voltage divider to increase lifespan
Terminating voltage by dropping it over large power resistors is a bad idea, efficiency wise. There are better options.

Switch-mode Buck (=step down) converters are usually far more efficient than linear regulators. A linear regulator dumps the excess voltage in a resistor which converts the energy mainly into heat. A switch-mode converter works by switching on/off an inductance at the right time, which is far more efficient.

For step-up/step-down DC-DC converter theory look here, here and here. For a comparison for switch-mode against linear regulators look here.

A step-down converter module like the ones with a LM2596 should be good enough for you. See here on ebay.