Composites Between Adjacent Primes

[hv at crypt.org]

"Pfoertner, Hugo" <Hugo.Pfoertner at muc.mtu.de> wrote:
[...]
:If we divide each term by the corresponding terms of A052248, we get
:
:2 2 2 4 2 6 2 2 6 2 2 6 2 3 2 12 2 3 24 2 2 2 2 9 6 2 3 3 2 3 2 6 2 30 5
:2 2 4 2 36 3 64 2 18 2 2 2 12 8 3 48 3 2 2 3 54 2 2 6 3 2 3 24 2 2 2 2 12
:27 2 2 7 8 2 2 2 2 4 3 60 2 144 4 26 2 2 2 42 2 2 2 3 6 2 4 2 18 2 2 2 2
:2 30 3 2 3 3 120 4 10 2 6 2 2 6 15 4 5 60
:
:I don't know if this is of any use.
:"Composite between two primes with biggest prime factor, divided by this
:factor"
:Is there a better definition?

Maybe:
  least integer m such that p[n] < mq < p[n+1] for some prime q

(That also suggests the possibility of:
  least integer m such that p[n] < mq^k < p[n+1] for some prime q, integer k
and the corresponding sequence of q^k.)

Hugo V.