OFFSET
2,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 2..10001 (calculated using data from Claude Goutier; terms 2..1000 from Donovan Johnson)
Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
GĂ©rard P. Michon, Carmichael Multiples of Odd Primes.
EXAMPLE
561 is the first Carmichael number and its prime factors are 3, 11, 17 (2nd, 5th and 7th primes), so a(2), a(5) and a(7) are equal to 561. - Michel Marcus, Nov 07 2013
MATHEMATICA
c = Cases[Range[1, 10000000, 2], n_ /; Mod[n, CarmichaelLambda@ n] == 1 && ! PrimeQ@ n]; Table[First@ Select[c, Mod[#, Prime@ n] == 0 &], {n, 2, 16}] (* Michael De Vlieger, Aug 28 2015, after Artur Jasinski at A002997 *)
PROG
(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
isA002997(n)=n%2 && !isprime(n) && Korselt(n) && n>1
a(n) = my(pn=prime(n), cn = 31*pn); until (isA002997(cn+=2*pn), ); cn; \\ Michel Marcus, Nov 07 2013, improved by M. F. Hasler, Apr 14 2015
(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
a(n, p=prime(n))=my(m=lift(Mod(1/p, p-1)), c=max(m, 33)*p, mp=m*p); while(!isprime(c) && !Korselt(c), c+=mp); c \\ Charles R Greathouse IV, Apr 15 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Nov 25 2007
EXTENSIONS
More terms from Michel Marcus, Nov 07 2013
Escape clause added by Jianing Song, Dec 12 2021
STATUS
approved