Hydropronic Sequence?

Consider the following sequence of numbers

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 28, \dots

What number comes next?  The OEIS has no sequence beginning with these, which seems puzzling enough, but wait!  There’s more.

You might, like me, wonder if this sequence contains all perfect numbers.  Alas, \displaystyle 496 is not in this list.  Does it contain all triangular numbers?

Update: this list still confuses me.  It definitely contains all squares and pronics, but it also appears to contain all numbers of the form n(n+2).  Also, a big fat “no” concerning the triangular numbers: 55 is not “hydropronic.”  (btw, I really need a better word for these numbers.)

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3 thoughts on “Hydropronic Sequence?

  1. One observation: this sequence appears to be closed under multiplication. Someone should write some code that checks this. Also, the “Sprague” formula is 100% correct.

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