Given an integer 
,
the Payam number 
is the smallest positive odd integer 
such that for every positive integer 
, the number 
is not divisible by any 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 
, 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, 45, 2145, ... (OEIS
A083391).
