new sequences related to xyz=(n-x)(n-y)(n-z)

[Max]

I'm about adding some new sequences to OEIS and wonder if somebody like to compute, extend or generalize them.

The original sequence contains such integer n that there exist integers x,y,z from {1,2,...,n-1} for which
x*y*z = (n-x)*(n-y)*(n-z)
and factors x,y,z all differ from any of n-x,n-y,n-z (this is always the case for odd n; and x,y,z must differ from n/2 for even n).

The beginning of this sequence is (some terms may be missed, though):
15, 20, 24, 30, 35, 40, 42, 45, 48, 55, 56, 60, 63, 65, 66, 70, 72, 75, 77, 78, 80, 84, 85, 88, 90, 91, 96, 99, 100, 104, 105, 110, 112, 117, 119, 120

More restrictive condition for all x,y,z,n-x,n-y,n-z being distinct integers issues another sequence:
24, 35, 40, 42, 45, 48, 55, 56, 60, 63, 66, 70, 72, 77, 80, 84, 88, 90, 91, 96, 99, 104, 105, 110, 112, 117, 119, 120

There are derivatives from these sequences, namely, sequences of all products xyz:
300, 450, 840, 1080, 2400, 2940, 3600, 3780, 4200, 4320, 5280, 5400, 5880, 6270, 6720, 7560, 8100, ...
and
4200, 4320, 5280, 5400, 5880, 6270, 6720, 7560, 8100, 8640, 8910, 9360, 10560, 12150, 12675, 12852, ...
respectively.

There are also interesting subsequences of n having more than one triple x,y,z defined as above.

There is a way to get similar sequences increasing number of factors, e.g. such n that there are x,y,z,t from {1,2,...,n-1} for which
x*y*z*t = (n-x)*(n-y)*(n-z)*(n-t)
and integers x,y,z,t all differ from any of n-x,n-y,n-z,n-t.
and so on.

Feel free to contribute either of these sequences to OEIS.

Max