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 A087788 3-Carmichael numbers: Carmichael numbers equal to the product of 3 primes: n=pqr, where p
 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; text; internal format)
 OFFSET 1,1 COMMENTS It is interesting that most of the numbers have the last digit 1. For example 530881, 3581761, 7207201, etc. Granville & Pomerance conjecture that there are ~ c x^{1/3}/(log x)^3 members of this sequence up to x. Heath-Brown proves that, for any e > 0, there are O(x^{7/20 + e}) members of this sequence up to x. - Charles R Greathouse IV, Nov 19 2012 REFERENCES O. Ore, Number Theory and Its History, McGraw-Hill, 1948, Reprinted by Dover Publications, 1988, Chapter 14. LINKS R. J. Mathar and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 3284 terms from Mathar) 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. Harvey Dubner, Journal of Integer Sequences, Vol. 5 (2002) Article 02.2.1, Carmichael Numbers of the form (6m+1)(12m+1)(18m+1). A. Granville and C. Pomerance, Two contradictory conjectures concerning Carmichael numbers, Math. Comp. 71 (2002), pp. 883-90. D. R. Heath-Brown, Carmichael numbers with three prime factors, Hardy-Ramanujan Journal 30 (2007), pp. 6-12. G. Jaeschke, The Carmichael numbers to 10^12, Math. Comp., 55 (1990), 383-389. Math Reference Project, Carmichael Numbers R. G. E. Pinch, Carmichael numbers up to 10^16 (FTP) Rosetta Code, Programs for finding 3-Carmichael numbers 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. 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. PROG (PARI) list(lim)=my(v=List()); forprime(p=3, (lim)^(1/3), forprime(q=p+1, sqrt(lim\p), forprime(r=q+1, lim\(p*q), if((q*r-1)%(p-1)||(p*r-1)%(q-1)||(p*q-1)%(r-1), , listput(v, p*q*r))))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Nov 19 2012 CROSSREFS Cf. A002997, A162290. Sequence in context: A309235 A104016 A002997 * A173703 A306338 A300629 Adjacent sequences:  A087785 A087786 A087787 * A087789 A087790 A087791 KEYWORD easy,nonn AUTHOR Miklos Kristof, Oct 07 2003 EXTENSIONS Minor edit to definition by N. J. A. Sloane, Sep 14 2009 STATUS approved

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Last modified September 15 18:22 EDT 2019. Contains 327082 sequences. (Running on oeis4.)