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A087788
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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.
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7
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561, 1105, 1729, 2465, 2821, 6601, 8911, 10585, 15841, 29341, 46657, 52633, 115921, 162401, 252601, 294409, 314821, 334153, 399001, 410041, 488881, 512461, 530881, 1024651, 1152271, 1193221, 1461241, 1615681, 1857241, 1909001, 2508013
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It is interesting that most of the numbers have the last digit 1. For example 530881, 3581761, 7207201, etc.
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REFERENCES
| 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.
G. Jaeschke, The Carmichael numbers to 10^12, Math. Comp., 55 (1990), 383-389.
O. Ore, Number Theory and Its History, McGraw-Hill, 1948, Reprinted by Dover Publications, 1988, Chapter 14.
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LINKS
| R. J. Mathar, Table of n, a(n) for n = 1..3284
Harvey Dubner, Journal of Integer Sequences, Vol. 5 (2002) Article 02.2.1, Carmichael Numbers of the form (6m+1)(12m+1)(18m+1).
Math Reference Project, Carmichael Numbers
R. G. E. Pinch, Carmichael numbers up to 10^16 (FTP)
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FORMULA
| n is composite and squarefree 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.
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A002997, A162290.
Sequence in context: A006971 A104016 A002997 * A173703 A083733 A175737
Adjacent sequences: A087785 A087786 A087787 * A087789 A087790 A087791
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Oct 07 2003
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EXTENSIONS
| Minor edit to definition by N. J. A. Sloane, Sep 14 2009
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