I have not tried hard to prove any of the assertions I make here. I figured, before I tried, to find out how much of this is well-known. The "abundancy index" of a natural number is the sum of its divisors, divided by the number itself. For classical perfect numbers, the abundancy index is 2; for multiperfect numbers in general, the abundancy index is an integer. The "superabundant numbers" (https://oeis.org/A004394) are record-setters for abundancy index; a number is in A004394 if its abundancy index exceeds that of all smaller numbers. It is easy to show that the superabundant numbers are a subsequence of the "prime signature leaders" (https://oeis.org/A025487), which I call "generalized primorials" for reasons that I think I have sketched here in the past. (A quick search fails to find the occasion, though.) The foregoing is uncontroversial. My speculations start here. Every superabundant number can be factored uniquely into primorials; this property is inherited from the generalized primorials. Apparently, the largest primorial factor of the superabundant numbers ascends smoothly, without ever retreating. It is 1 for n=1, 2 up through n=3, 6 up through n=8, 30 up through n=14, and 210 up through n=22 (I think). A less mysterious way to say this is that if a superabundant number is divisible by a prime p, all larger superabundant numbers are also divisible by p. Let p# be the largest primorial dividing a superabundant number n. Then n/p# is a "cofactor"; the cofactors of the superabundant numbers in order are: 1,1,2,1,2,4,6,8,2,4,6,8,12,24,4,6... This is not in OEIS. It looks like these cofactors all belong to another sequence, 1,2,4,6,8,12,24,48,72,120; within each primorial "period", the cofactors march up this sequence in order, resetting to a lower value when a new period starts. This sequence of cofactors is also not in OEIS. If these speculations are true, then the sequence of superabundant numbers can be compressed by giving the starting index of each period, and the starting index of the cofactor sequence. But this leaves the cofactor sequence inadequately characterized.