A293291 Carmichael numbers m having a Fermat prime (A019434) factor such that A002322(m) = 2^k * p^2, where k is an integer and p is an odd prime.

825265, 1210178305, 11113519105, 230864201601, 772350315265, 1540032424705, 204855497662465, 453644962192318465, 770522162068767745, 3070111619849131585, 44428201205269571987560724263876473913345

Offset: 1

Author

Max Alekseyev, Oct 05 2017

Keywords

• nonn

Comments

Tsumura (2017) proved that there are no other such Carmichael numbers if there are only five Fermat primes.

The prime p happens to equal 3 or 5 in all cases.

Links

• Y. Tsumura, On the finiteness of Carmichael numbers with Fermat factors and L = 2^α P^2, arXiv:1710.01321 [math.NT], 2017.

Crossrefs

Cf. A002997, A214428.