Three ancient immortal beings float together in the vast emptiness of space... Unable to die, and looking for ways to pass the time.  The first Titan's name is fifteen, the second Titan is named seventeen, and the third is named twenty-three.  These mathematical Titans are each obsessed by the number they were named after, and are bound to them in strange and magical ways.

When attempting to count the stars around them, the three quickly realized that even their combined efforts could not quite do the job.  The titans had no way of expressing numbers 1 through 14, or number 16.  As they continued counting they failed at everything except 15, 17, 23, and finally 38.  When they reached 32 stars, the Titans fifteen and seventeen worked together.  As it turned out, Titans failed to express any number that wasn't some combination of their 3 names.  Titan fifteen was able to express the number 90 because it is exactly his name 6 times.  Titans seventeen and twenty-three were able to express the number 80 because it was each of their names twice, combined.

The Titans were so frustrated when they started to count the stars, that they almost gave up.  Fortunately they kept going and as time went on they ran into fewer and fewer numbers they couldn't express.  Eventually they reached 50, and once again couldn't figure out a way to express the number.  This was the point when the trio of Titans paused to wonder...

If they continued counting up to 100, what was the largest number they wouldn't be able to express?