Payam Number
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).
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