1,1

a(n) includes all Carmichael numbers A002997(n) = {561,1105,1729,2465,2821,6601,8911,10585,15841,29341,...}: composite numbers n such that a^{n-1} = 1 ( mod n) if a is prime to n.

Prime p divides 3^p - 2^p - 1. Quotients (3^p - 2^p - 1)/p, where p = Prime[n], are listed in A127071(n) = {2,6,42,294,15918,122010,7588770,61144062,4092816966,2366546223930,...}. Numbers n such that n divides 3^n - 2^n - 1 are listed in A127072(n) = {1,2,3,4,5,7,8,9,11,13,16,17,19,23,27,29,31,32,37,41,43,45,47,49,53,59,61,64,67,71,73,79,81,83,89,97,...}. Pseudoprimes in A127072(n) include all powers of primes {2,3,7} and some composite numbers that are listed in a(n). Numbers n such that n^2 divides 3^n - 2^n - 1 are listed in A127074(n) = {1,2,3,4,7,49,179,619,...}. Numbers n such that n^3 divides 3^n - 2^n - 1 are {1,4,7,...}.

Eric Weisstein, Link to a section of The World of Mathematics. Carmichael number.

Eric Weisstein, Link to a section of The World of Mathematics. Pseudoprime.

Select[Select[Range[2^15], !PrimeQ[ # ]&&IntegerQ[(3^#-2^#-1)/# ]&], !IntegerQ[Log[2, # ]]&&!IntegerQ[Log[3, # ]]&&!IntegerQ[Log[7, # ]]&]

Cf. A002997 = Carmichael numbers.

Cf. A127071, A127072, A127074.

Sequence in context: A091197 A146302 A087442 this_sequence A089549 A064561 A093761

Adjacent sequences: A127070 A127071 A127072 this_sequence A127074 A127075 A127076

nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Jan 04 2007