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A033502 Carmichael numbers of the form (6*k+1)*(12*k+1)*(18*k+1), where 6*k+1, 12*k+1 and 18*k+1 are all primes. 10
1729, 294409, 56052361, 118901521, 172947529, 216821881, 228842209, 1299963601, 2301745249, 9624742921, 11346205609, 13079177569, 21515221081, 27278026129, 65700513721, 71171308081, 100264053529, 168003672409, 172018713961, 173032371289, 464052305161 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also called Chernick's Carmichael numbers.

The first term, 1729, is the Hardy-Ramanujan number.

Dickson's conjecture implies that this sequence is infinite, as pointed out by Chernick.

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, A13.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..10000

Jack Chernick, On Fermat's simple theorem, Bull. Amer. Math. Soc. 45:4 (1939), pp. 269-274.

G. Tarry, I. Franel, A. Korselt, and G. Vacca. Problème chinois. L'intermédiaire des mathématiciens 6 (1899), pp. 142-144.

Eric Weisstein's World of Mathematics, Carmichael Number

Index entries for sequences related to Carmichael numbers.

MATHEMATICA

CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; (6# + 1)(12# + 1)(18# + 1) & /@

Select[ Range@ 1000, PrimeQ[6# + 1] && PrimeQ[12# + 1] && PrimeQ[18# + 1] && CarmichaelNbrQ[(6# + 1)(12# + 1)(18# + 1)] &]

PROG

(MAGMA) [n : k in [1..710] | IsPrime(a) and IsPrime(b) and IsPrime(c) and IsOne(n mod CarmichaelLambda(n)) where n is a*b*c where a is 6*k+1 where b is 12*k+1 where c is 18*k+1]; // Arkadiusz Wesolowski, Oct 29 2013

CROSSREFS

Values of k are given by A046025. See also A002997.

Cf. A242980, A242981.

Sequence in context: A272798 A212920 A182087 * A277366 A050794 A138130

Adjacent sequences:  A033499 A033500 A033501 * A033503 A033504 A033505

KEYWORD

nonn

AUTHOR

Marc LeBrun

EXTENSIONS

Definition corrected (thanks to Umberto Cerruti) by Bruno Berselli, Jan 18 2013

STATUS

approved

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Last modified May 23 18:42 EDT 2017. Contains 286926 sequences.