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%I A285549 #41 Nov 14 2022 05:57:27
%S A285549 341,2701,721801,721801,42702661,1112103541,2380603501,5202153001,
%T A285549 17231383261,251994268081,1729579597021,55181730338101,
%U A285549 142621888086541,242017633321201,242017633321201,242017633321201,1174858593838021,1174858593838021,168562580058457201,790489610041255741,790489610041255741,790489610041255741
%N A285549 Smallest weak pseudoprime to all natural bases up to prime(n) that is not a Carmichael number.
%C A285549 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 A285549 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 A285549 a(23) > 2^64. - _Max Alekseyev_, Apr 22 2017
%C A285549 Conjecture: lpf(a(n)) > prime(n), where lpf = A020639. - _Thomas Ordowski_, May 13 2017
%C A285549 Except a(19), the listed terms are semiprime. - _Thomas Ordowski_, Feb 09 2018
%C A285549 a(24) <= 21150412877533909683421, a(362) <= (416*A002110(360) + 1) * (832*A002110(360) + 1). - _Daniel Suteu_, Nov 13 2022
%Y A285549 Cf. A002997, A020639, A083876, A285512.
%K A285549 nonn
%O A285549 1,1
%A A285549 _Thomas Ordowski_, Apr 21 2017
%E A285549 a(5)-a(9) from _Giovanni Resta_, Apr 21 2017
%E A285549 a(10)-a(22) from _Max Alekseyev_, Apr 22 2017

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