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A006931 Least Carmichael number with n prime factors.
(Formerly M5463)
561, 41041, 825265, 321197185, 5394826801, 232250619601, 9746347772161, 1436697831295441, 60977817398996785, 7156857700403137441, 1791562810662585767521, 87674969936234821377601 (list; graph; refs; listen; history; text; internal format)



Alford, Grantham, Hayman, & Shallue construct large Carmichael numbers, finding upper bounds for a(3)-a(19565220) and a(10333229505). - Charles R Greathouse IV, May 30 2013


J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), p. 269, Pour la Science, Paris 2000.

R. G. E. Pinch, The Carmichael numbers up to 10^15. Math. Comp. 61 (1993), no. 203, 381-391.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


David W. Wilson, Table of n, a(n) for n = 3..35

W. R. Alford, Jon Grantham, Steven Hayman, Andrew Shallue, Constructing Carmichael numbers through improved subset-product algorithms, arXiv:1203.6664 (2012).

R. G. E. Pinch, The Carmichael numbers up to 10^17

R. G. E. Pinch, The Carmichael numbers up to 10^18

Eric Weisstein's World of Mathematics, Carmichael Number

Index entries for sequences related to Carmichael numbers.


(PARI) Korselt(n, f=factor(n))=for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1

a(n)=my(p=2, f); forprime(q=3, default(primelimit), forstep(k=p+2, q-2, 2, f=factor(k); if(vecmax(f[, 2])==1 && #f[, 2]==n && Korselt(k, f), return(k))); p=q)

\\ Charles R Greathouse IV, Apr 25 2012


Cf. A002997, A135717, A135719, A135720, A135721.

Cf. A087788, A141711, A074379, A112428, A112429, A112430, A112431, A112432.

Sequence in context: A264214 A083736 A182090 * A258801 A097061 A258839

Adjacent sequences:  A006928 A006929 A006930 * A006932 A006933 A006934




N. J. A. Sloane and Richard Pinch


Corrected by Lekraj Beedassy, Dec 31 2002

More terms from Ralf Stephan, from the Pinch paper, Apr 16 2005

Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar.



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Last modified November 26 22:04 EST 2015. Contains 264511 sequences.