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 :

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

  2. 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.


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