A289338 Composite numbers (pseudoprimes) n, that are not Carmichael numbers, such that A000670(n) == 1 (mod n).

169, 885, 2193, 8905, 22713

Offset: 1

Author

Amiram Eldar, Jul 02 2017

Keywords

• nonn
• more

Comments

I. J. Good proved that A000670(n) == A000670(m) (mod p) for all primes p, and n == m (mod p-1). Therefore the congruence A000670(n) == 1 (mod n) holds for all primes and Carmichael numbers. This sequence consist of the other composite numbers for which the congruence holds.

Links

• I. J. Good, The number of orderings of n candidates when ties are permitted, Fibonacci Quarterly, Vol. 13 (1975), pp. 11-18.

Crossrefs

Cf. A000670, A002997, A289337.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k]*a[n - k], {k, 1, n}]; carmichaelQ[n_]:=(Mod[n, CarmichaelLambda[n]] == 1); seqQ[n_] := !PrimeQ[n] && !carmichaelQ[n] && Divisible[a[n]-1,n]; Select[Range[2,500],seqQ]