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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.
1

%I #8 Aug 27 2021 01:47:15

%S 825265,1210178305,11113519105,230864201601,772350315265,

%T 1540032424705,204855497662465,453644962192318465,770522162068767745,

%U 3070111619849131585,44428201205269571987560724263876473913345

%N 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.

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

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

%H Y. Tsumura, <a href="https://arxiv.org/abs/1710.01321">On the finiteness of Carmichael numbers with Fermat factors and L = 2^α P^2</a>, arXiv:1710.01321 [math.NT], 2017.

%Y Cf. A002997, A214428.

%K nonn

%O 1,1

%A _Max Alekseyev_, Oct 05 2017