Search: id:A087788
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%I A087788
%S A087788 561,1105,1729,2465,2821,6601,8911,10585,15841,29341,46657,52633,115921,
%T A087788 162401,252601,294409,314821,334153,399001,410041,488881,512461,530881,
%U A087788 1024651,1152271,1193221,1461241,1615681,1857241,1909001,2508013
%N A087788 3-Carmichael numbers: Carmichael numbers equal to the product of 3 primes: 
               n=pqr, where p<q<r are primes such that a^{n-1} == 1 (mod n) if a 
               is prime to n.
%C A087788 It is interesting that most of the numbers have the last digit 1. For 
               example 530881, 3581761, 7207201, etc.
%D A087788 F. Arnault, Constructing Carmichael numbers which are strong pseudoprimes 
               to several bases, Journal of Symbolic Computation, vol. 20, no 2, 
               Aug. 1995, pp. 151-161.
%D A087788 G. Jaeschke, The Carmichael numbers to 10^12, Math. Comp., 55 (1990), 
               383-389.
%D A087788 O. Ore, Number Theory and Its History, McGraw-Hill, 1948, Reprinted by 
               Dover Publications, 1988, Chapter 14.
%H A087788 Harvey Dubner, Journal of Integer Sequences, Vol. 5 (2002) Article 02.2.1, 
               <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Dubner/dubner6.html">
               Carmichael Numbers of the form (6m+1)(12m+1)(18m+1).</a>
%H A087788 Math Reference Project, <a href="http://www.mathreference.com/num-mod,
               ccm.html">Carmichael Numbers</a>
%H A087788 R. G. E. Pinch, <a href="ftp://ftp.dpmms.cam.ac.uk/pub/Carmichael/">Carmichael 
               numbers up to 10^16 (FTP)</a>
%F A087788 n is composite and square-free and for p prime, p|n => p-1|n-1. A composite 
               odd number n is a Carmichael number if and only if n is squarefree 
               and p-1 divides n-1 for every prime p dividing n (Korselt, 1899) 
               n=pqr, p-1|n-1, q-1|n-1, r-1|n-1.
%e A087788 a(6)=6601=7*23*41: 7-1|6601-1, 23-1|6601-1, 41-1|6601-1, i.e. 6|6600, 
               22|6600, 40|6600.
%Y A087788 Cf. A002997, A162290.
%Y A087788 Sequence in context: A006971 A104016 A002997 this_sequence A083733 A048123 
               A131672
%Y A087788 Adjacent sequences: A087785 A087786 A087787 this_sequence A087789 A087790 
               A087791
%K A087788 easy,nonn
%O A087788 1,1
%A A087788 Miklos Kristof (kristmikl(AT)freemail.hu), Oct 07 2003
%E A087788 Minor edit to definition by N. J. A. Sloane, Sep 14 2009

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