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Carmichael numbers of the form (6*k + 1)*(12*k + 1)*(18*k + 1), where only two of the three numbers 6*k + 1, 12*k + 1, 18*k + 1 are prime.
3

%I #12 Sep 08 2022 08:46:08

%S 172081,1773289,4463641,47006785,295643089,798770161,1150270849,

%T 1420379065,1976295241,18390744505,122160500281,134642101321,

%U 215741809801,228944441089,263610459505,321140603665,374464040689,444722065201,676328168881,1009514855521

%N Carmichael numbers of the form (6*k + 1)*(12*k + 1)*(18*k + 1), where only two of the three numbers 6*k + 1, 12*k + 1, 18*k + 1 are prime.

%H Giovanni Resta, <a href="/A242980/b242980.txt">Table of n, a(n) for n = 1..2665</a> (terms < 4*10^30)

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_739.htm">Puzzle 739</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelNumber.html">Carmichael Number</a>

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

%o (Magma) lst:=[]; for k in [1..920] do t:={n: n in [1..3] | IsPrime(6*k*n+1)}; if #Set(t) eq 2 then c:=&*[6*k*n+1: n in [1..3]]; if IsOne(c mod CarmichaelLambda(c)) then lst:=Append(lst, c); end if; end if; end for; lst;

%Y Cf. A002997, A033502, A242981.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, May 28 2014