The Payam number 
,
for an integer 
, is the smallest positive odd integer 
such that for every positive
integer 
,
the number 
is not divisible by any odd primes 
such that the multiplicative
order of 2 
is less than or equal to 
.
Payam numbers are good candidates for searching for Proth
primes, i.e., primes of the form 
with 
, as well as primes
of the form 
.
The first few values of 
for 
, 3, ... are 3, 9, 15, 105, 105, 105,
105, 105, 165, 165, 75075, ... (OEIS A083556),
and the first few values of 
are 3, 3, 45, 45, 45, 45, 45, 45, 2145, ... (OEIS A083391).
