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Carmichael numbers with more than 3 prime factors.
8

%I #16 Jun 25 2019 10:48:34

%S 41041,62745,63973,75361,101101,126217,172081,188461,278545,340561,

%T 449065,552721,656601,658801,670033,748657,825265,838201,852841,

%U 997633,1033669,1050985,1082809,1569457,1773289,2100901,2113921,2433601

%N Carmichael numbers with more than 3 prime factors.

%C Sequence A087788 gives Carmichael numbers with exactly 3 prime factors; since they cannot have fewer (cf. references in A002997), this sequence is the complement of A087788 in A002997.

%C The terms preceding a(17) = 825265 = A006931(5) have exactly 4 prime factors. See A112428 - A112432 for Carmichael numbers with exactly 5, ..., 9 prime factors. - _M. F. Hasler_, Apr 14 2015

%H Amiram Eldar, <a href="/A141711/b141711.txt">Table of n, a(n) for n = 1..10000</a>

%F A141711 = A002997 \ A087788 = A074379 U A112428 U A112429 U A112430 U A112431 U A112432 U ...

%e a(17)=825265 is the least Carmichael number having more than 4 divisors, thus the sequence differs from A074379 only from that term on.

%t ok[n_] := Divisible[n - 1, CarmichaelLambda[n]] && Length[FactorInteger[n]] > 3; Select[ Range[3*10^6], ok] (* _Jean-François Alcover_, Sep 23 2011 *)

%o (PARI) A2997=readvec("b002997.gp"); A002997(n)=A2997[n]; for( n=1,100, omega( A002997(n) ) > 3 & print1( A002997(n)", "))

%Y Cf. A002997, A087788, A074379, A112428 - A112432, A006931.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jul 01 2008