A029560 - OEIS

%I #19 Sep 16 2015 01:52:08

%S 35,1295,2635,6083,6923,7315,7843,13363,24335,25795,26243,29795,31003,

%T 43043,44099,49283,50435,54131,115843,138043,147223,191843,234883,

%U 254467,388433,471523,472739,544643,618103,631123,725903,790195,819283,862403

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

%C 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).

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

%H Giovanni Resta, <a href="/A029560/b029560.txt">Table of n, a(n) for n = 1..2453</a> (terms < 10^12)

%H K. Bouallegue, O. Echi, R. G. E. Pinch, <a href="http://dx.doi.org/10.1142/S1793042110002922 ">Korselt numbers and sets</a>, Intl. J. Numb. Theory 6 (2) (2010) 257-269.

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

%t 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 *)

%Y Cf. A120944

%K nonn

%O 1,1

%A _David W. Wilson_