A182817 Number of elements k in Z/mZ such that k^m=k, for nonprime m = A018252(n).

1, 2, 4, 2, 3, 4, 4, 4, 9, 2, 4, 4, 9, 4, 4, 5, 4, 3, 8, 8, 2, 9, 4, 9, 4, 4, 9, 4, 8, 4, 15, 4, 4, 7, 4, 9, 8, 4, 9, 4, 9, 4, 8, 4, 9, 2, 25, 24, 4, 9, 16, 4, 4, 9, 8, 9, 8, 4, 3, 4, 8, 25, 4, 9, 4, 8, 49, 4, 9, 4, 9, 4, 4, 9, 4, 8, 4, 45, 4, 4, 8, 9, 8, 8, 9, 4, 15, 4, 9, 8, 11, 4, 9, 8, 5, 8, 2, 9, 16, 8, 49, 4, 9, 4, 8, 8, 9, 4, 9, 4, 25, 4, 9, 8, 8, 4, 27, 16, 9, 8, 4, 9, 4, 9, 4

Offset: 1

Author

M. F. Hasler, Dec 05 2010

Keywords

• nonn

Comments

This is a reduced version of A182816, without the "trivial" terms a(n)=n for prime indices n.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• "Lunkwill", Carmichael numbers and Fermat primality, Dec 02 2010.

Crossrefs

Cf. A018252, A182816, A002997.

Programs

Mathematica

f[n_] := Times @@ ((1 + GCD[n-1, #-1]) & /@ FactorInteger[n][[;;,1]]); f /@ Select[Range[165], !PrimeQ[#] &] (* Amiram Eldar, Mar 27 2021 *)

Formula

a(n) = A182816(A018252(n)).