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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. 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 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 EXTENSIONS Definition corrected (thanks to Umberto Cerruti) by Bruno Berselli, Jan 18 2013 STATUS approved

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Last modified April 13 10:24 EDT 2021. Contains 342935 sequences. (Running on oeis4.)