A328939 - OEIS

%I #15 Apr 22 2024 14:28:25

%S 10267951,72108421,111291181,139952671,1588247851,6004532941,

%T 7200256261,8815102297,9001235881,10884042841,15989367241,18500666251,

%U 23729234761,34268731321,34558584607,37870128451,74689102411,77538554731,121254376891,149842746691,187054437571

%N Carmichael numbers that are products of primes p for which each p-1 is squarefree.

%C Shanks noted that among the first 300 Carmichael numbers only 3 are in this sequence.

%H Amiram Eldar, <a href="/A328939/b328939.txt">Table of n, a(n) for n = 1..10000</a> (calculated using data from Claude Goutier)

%H Paul Erdős, <a href="https://renyi.hu/~p_erdos/1956-10.pdf">On pseudoprimes and Carmichael numbers</a>, Publ. Math. Debrecen 4 (1956), pp. 201-206.

%H Claude Goutier, <a href="http://www-labs.iro.umontreal.ca/~goutier/OEIS/A055553/">Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22</a>.

%H Andrew Granville and Carl Pomerance, <a href="https://doi.org/10.1090/S0025-5718-01-01355-2">Two contradictory conjectures concerning Carmichael numbers</a>, Mathematics of Computation, Vol. 71, No. 238 (2002), pp. 883-908.

%H Daniel Shanks, <a href="https://archive.org/details/SolvedAndUnsolvedProblemsInNumberTheory/page/n239">Solved and Unsolved Problems in Number Theory</a>, 2nd ed., Chelsea Pub. Co., New York, 1978, p. 229.

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.

%t aQ[n_] := CompositeQ[n] && Divisible[n-1, CarmichaelLambda[n]] && AllTrue[FactorInteger[n][[;; , 1]] - 1, SquareFreeQ]; Select[Range[10^8], aQ]

%Y Cf. A002997.

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 31 2019