Several things to do relating tax when setting up a company in Japan.

The first thing you need to do is to let a tax office know that you set up a company. There are many national and local tax offices so you should check which office covers your company (depends on where your company is located). This report needs to be submitted to your tax office within two months after your company was set up. Also, copies of articles of incorporation and certificate of commercial registration are needed (some additional documents may be needed when tax office asks).

This application is not mandatory but generally almost all companies submit it, as there are several advantages of tax calculation. One of the biggest advantages is 'Tax loss carryforward'. This means that the realised losses can offset the gains for the next nine (or ten) years. This would lead to significantly lowering tax payments. 

And there might be no disadvantage of this application (professional accounting record, etc, is needed though). This is why almost all companies submit it.

Your company has employees (in future). Then you need to tell tax office about it, as withholding income tax should be deducted from emloyees' salaries and paid to tax office every month. 

It is hard for small companies to make payments of withholding income tax every month. If you submit this application, you are allowed to pay taxes every six month. Withholding income taxes for January to June are paid in July, and taxes for July to December are paid in January. A small company means it has less than ten employees.