Solution #14
Oh, I completely forgot I’d posted this. Guess the solution wasn’t tomorrow after all.
Either way, it’s below the line
The sequence is the smallest numbers that divide by every natural number up to 1, 2, 3, 4, 5... etc. up to 360360 being the smallest number that will divide by every natural number up to 13. The next three numbers in the sequence are: 360360 (smallest number that divides by every natural number up to 14) 360360 (ditto 15) 720720 (ditto 16)
There are several repeated numbers in the sequence because these numbers are already “covered” somehow - as you might expect, the biggest jumps in the sequence are when a new prime shows up, with smaller jumps being for when another factor of 2 or 3 needs to be added.
The nice repeating digits patterns for 360360 and 720720 come from the fact that 1001 happens to equal 7 x 11 x 13 - as such, any number with digits abcabc is also going to divide by these three numbers. Since 360 divides by every number up to 15 excluding those three, 360360 is going to be the smallest number that divides by every number up to 15.
Perhaps unsurprisingly, several - though not all - of the numbers in this sequence are on the sequences of superior highly composite numbers and colossally abundant numbers. I’m not entirely sure what the formal definitions of these numbers mean, but it’s pretty clear that they have a gosh-dang high number of factors. 2, 6, 12, 60, 2520 and 720720 show up on both these lists, as do some of their multiples
Anyone fancy counting in base 720720?
