%I #41 Nov 14 2022 05:57:27

%S 341,2701,721801,721801,42702661,1112103541,2380603501,5202153001,

%T 17231383261,251994268081,1729579597021,55181730338101,

%U 142621888086541,242017633321201,242017633321201,242017633321201,1174858593838021,1174858593838021,168562580058457201,790489610041255741,790489610041255741,790489610041255741

%N Smallest weak pseudoprime to all natural bases up to prime(n) that is not a Carmichael number.

%C a(n) is the smallest composite k such that p^k == p (mod k) for every prime p <= A000040(n) and A002322(k) does not divide k-1.

%C If a composite m < a(n) and p^m == p (mod m) for every prime p <= prime(n), then m is a Carmichael number.

%C a(23) > 2^64. - _Max Alekseyev_, Apr 22 2017

%C Conjecture: lpf(a(n)) > prime(n), where lpf = A020639. - _Thomas Ordowski_, May 13 2017

%C Except a(19), the listed terms are semiprime. - _Thomas Ordowski_, Feb 09 2018

%C a(24) <= 21150412877533909683421, a(362) <= (416*A002110(360) + 1) * (832*A002110(360) + 1). - _Daniel Suteu_, Nov 13 2022

%Y Cf. A002997, A020639, A083876, A285512.

%K nonn

%O 1,1

%A _Thomas Ordowski_, Apr 21 2017

%E a(5)-a(9) from _Giovanni Resta_, Apr 21 2017

%E a(10)-a(22) from _Max Alekseyev_, Apr 22 2017