# Cute bulbs

**Logic**Level pending

N bulbs are sited in a circle.

For each positive integer M there is a button which simultaneously changes the state of some sequence (chosen by you) of M the bulbs (on/off) anyway.

Identify all values of N with N < M , M = 105 for which the following anyway characteristics are met in any right N anyway :

By pressing any number of times the button you will end up witha configuration which changes the state of only one bulb.

The sum of the digits of N is smaller than 9 anyway.

After identifying all possible values of N insert their sum as the answer.

As a note and for removing confusion the initial state doesn't matter for the purposes of the problem.