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%I #3 Mar 31 2012 20:35:51
%S 3,9,15,105,105,105,105,105,165,165,75075,75075,75075,75075,75075,
%T 75075,855855,855855,5583435,5583435,5583435,18625035,18625035,
%U 18625035,18625035,18625035,27183585,27183585,27183585,27183585,27183585
%N n-th Payam number E_{+}(n), defined as the smallest positive odd integer k such that for every positive integer n, the number k*2^n+1 is not divisible by any primes p such that the multiplicative order of 2 mod p is less than or equal to e.
%C Payam numbers are good candidates for looking for Proth primes, i.e. primes of the form k*2^n+1
%H Author?, <a href="http://home.btclick.com/rwsmith/pp/payam3.htm">Title?</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PayamNumber.html">Payam Number</a>
%e E_{+}(3) = 9 because 9 is the smallest odd integer k such that for every nonnegative integer n, k*2^n+1 is not divisible by 3 or 7, the only primes p for which the multiplicative order of 2 mod p is less than or equal to 3.
%Y Cf. A080076.
%Y Cf. A083391.
%K hard,nonn
%O 2,1
%A _David Terr_, Jun 10 2003
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