login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 16
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.

D. E. Iannucci, When the small divisors of a natural number are in arithmetic progression, INTEGERS, Electronic Journal of Combinatorial Number Theory, #77, 2018. See p. 9.

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: A318646 A182087 A327787 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 15:26 EST 2020. Contains 332137 sequences. (Running on oeis4.)