A285549 Smallest weak pseudoprime to all natural bases up to prime(n) that is not a Carmichael number.

341, 2701, 721801, 721801, 42702661, 1112103541, 2380603501, 5202153001, 17231383261, 251994268081, 1729579597021, 55181730338101, 142621888086541, 242017633321201, 242017633321201, 242017633321201, 1174858593838021, 1174858593838021, 168562580058457201, 790489610041255741, 790489610041255741, 790489610041255741

Offset: 1

Author

Thomas Ordowski, Apr 21 2017

Keywords

• nonn

Comments

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.

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

a(23) > 2^64. - Max Alekseyev, Apr 22 2017

Conjecture: lpf(a(n)) > prime(n), where lpf = A020639. - Thomas Ordowski, May 13 2017

Except a(19), the listed terms are semiprime. - Thomas Ordowski, Feb 09 2018

a(24) <= 21150412877533909683421, a(362) <= (416*A002110(360) + 1) * (832*A002110(360) + 1). - Daniel Suteu, Nov 13 2022

Crossrefs

Cf. A002997, A020639, A083876, A285512.

Extensions

a(5)-a(9) from Giovanni Resta, Apr 21 2017

a(10)-a(22) from Max Alekseyev, Apr 22 2017