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

1,1

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

Links

Table of n, a(n) for n=1..22.

Crossrefs

Cf. A002997, A020639, A083876, A285512.

Sequence in context: A354694 A143688 A086250 * A306310 A210454 A069309

Adjacent sequences: A285546 A285547 A285548 * A285550 A285551 A285552

Keyword

nonn

Author

Thomas Ordowski, Apr 21 2017

Extensions

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

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

Status

approved