Intended for: April 19, 2014
Timetable
- First draft entered by Peter Luschny on April 1, 2013 ✓
- Draft reviewed by Alonso del Arte on April 2, 2013 ✓
- Draft approved by Daniel Forgues on April 10, 2013 ✓
The line below marks the end of the <noinclude> ... </noinclude> section.
A092287:
.
-
{ 1, 1, 2, 6, 96, 480, 414720, 2903040, ... }
Peter Bala conjectures that the order of the
primes in the
prime factorization of
is given by the formula
- Charles R Greathouse IV proved Bala's conjecture very recently.
Comparing this with the
de Polignac–Legendre formula for the prime factorization of
, i.e.
-
this suggests that
can be considered as a "generalization of the
factorial numbers" * (the product between braces is obviously
1 if
is
noncomposite)
-
Recurrence:
-
Formula:
-
A??????
.
-
{1, 1, 1, 1, 4, 4, 576, 576, 147456, 11943936, 76441190400, 76441190400,...}
A224479 .
-
{1, 1, 1, 1, 2, 2, 24, 24, 384, 3456, 276480, 276480, 955514880, 955514880, ...}
-------------------------
* See GCD matrix generalization of the factorial.