A328939 Carmichael numbers that are products of primes p for which each p-1 is squarefree.

10267951, 72108421, 111291181, 139952671, 1588247851, 6004532941, 7200256261, 8815102297, 9001235881, 10884042841, 15989367241, 18500666251, 23729234761, 34268731321, 34558584607, 37870128451, 74689102411, 77538554731, 121254376891, 149842746691, 187054437571

Offset: 1

Author

Amiram Eldar, Oct 31 2019

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Claude Goutier)
• Paul Erdős, On pseudoprimes and Carmichael numbers, Publ. Math. Debrecen 4 (1956), pp. 201-206.
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Andrew Granville and Carl Pomerance, Two contradictory conjectures concerning Carmichael numbers, Mathematics of Computation, Vol. 71, No. 238 (2002), pp. 883-908.
• Daniel Shanks, Solved and Unsolved Problems in Number Theory, 2nd ed., Chelsea Pub. Co., New York, 1978, p. 229.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A002997.

Programs

Mathematica

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