The 
th Monica set 
is defined as the set of composite
numbers 
for which ![n|[S(x)-S_p(x)]](/images/equations/MonicaSet/Inline4.svg)
,
where 
is a positive
integer. Write 
in decimal notation and as its prime factorization,
with prime factors repeated according to their multiplicity, as
 |  |  |
(1)
|
 |  |  |
(2)
|
and
 |  |  |
(3)
|
 |  |  |
(4)
|
Every Monica set has an infinite number of elements (Smith 1996).
The Monica set 
is a superset of the Suzanne
set 
.
The following table gives the first few Monica numbers in 
for small 
.
 | OEIS |  |
| 1 | A002808 | 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ... |
| 2 | A102218 | 4, 8, 10, 12, 14, 15, 22, 26, 27, 35, 42, 44, ... |
| 3 | A177927 | 4, 9, 10, 22, 24, 25, 27, 34, 42, 46, 55, 58, ... |
If 
is a Smith
number, then it is a member of the Monica set 
for all 
. For any integer 
, if 
is a 
-Smith number, then 
.
