The first few refactorable numbers are 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, ...
(OEIS A033950).
The first few
such that
and
are both refactorable numbers are 1, 8, 1520, 50624, 62000, 103040, ... (OEIS A114617).
Zelinsky (2002, pp. 7 and 15-16) proved that there are no refactorable numbers
and
such that
and also Colton's (1999) conjecture that no three
consecutive integers can all be refactorable.
that is divisible by the number
of its divisors 
, where 
is the divisor function.
such that 
and 
are both refactorable numbers are 1, 8, 1520, 50624, 62000, 103040, ... (OEIS A114617).
and 
such that 
and also Colton's (1999) conjecture that no three
consecutive integers can all be refactorable.
