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

1,1

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

Table of n, a(n) for n=1..11.

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.

Sequence in context: A112443 A112428 A182532 * A258516 A258509 A254996

Adjacent sequences: A293288 A293289 A293290 * A293292 A293293 A293294

Keyword

nonn

Author

Max Alekseyev, Oct 05 2017

Status

approved