A029560 Quasi-Carmichael numbers to base 3: squarefree composites n such that prime p|n ==> p-3|n-3.

35, 1295, 2635, 6083, 6923, 7315, 7843, 13363, 24335, 25795, 26243, 29795, 31003, 43043, 44099, 49283, 50435, 54131, 115843, 138043, 147223, 191843, 234883, 254467, 388433, 471523, 472739, 544643, 618103, 631123, 725903, 790195, 819283, 862403

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Define C(k) to be the numbers n such that n is composite and squarefree and for p prime, p|n => p+k|n+k (p+k and n+k positive); sequence gives C(-3).

These are called 3-Korselt numbers by Bouallegue et al.

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2453 (terms < 10^12)
• K. Bouallegue, O. Echi, R. G. E. Pinch, Korselt numbers and sets, Intl. J. Numb. Theory 6 (2) (2010) 257-269.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A120944

Programs

Mathematica

qcm[n_, d_] := Block[{p, e}, {p, e} = Transpose@FactorInteger@n; Length[p] > 1 && Max[e] == 1 && ! MemberQ[p, d] && Max@ Mod[n-d, p-d] == 0]; Select[Range[10^5],  qcm[#, 3] &] (* Giovanni Resta, May 21 2013 *)