A347946 Products of nonprimitive roots of n, or 0 if n = 2 or has no primitive roots.

0, 0, 1, 2, 4, 24, 48, 0, 4032, 17280, 5400, 0, 518400, 415134720, 0, 0, 1797120, 6467044147200, 39086530560, 0, 0, 1738201006080000, 10247897088, 0, 9632530575360000, 706822057112371200000, 569299069913333760000, 0, 54538738974720000, 0

Offset

1,4

Comments

If n is a prime p, a(n) == -1 (mod p) for n > 3; if n is a composite c, a(n) == 0 (mod c) for n > 4.

Links

Table of n, a(n) for n=1..30.

Example

a(11) = 5400 because the primitive roots of 11 are {2,6,7,8} and therefore the nonprimitive roots of 11 are {1,3,4,5,9,10} and 1*3*4*5*9*10 = 5400.

Mathematica

a[n_] := If[n == 2 || (p = PrimitiveRootList[n]) == {}, 0, (n - 1)!/Times @@ p]; Array[a, 30] (* Amiram Eldar, Sep 26 2021 *)

Crossrefs

Cf. A123475, A219027, A219028.

Sequence in context: A163896 A350813 A262698 * A168054 A280075 A068506

Adjacent sequences: A347943 A347944 A347945 * A347947 A347948 A347949

Keyword

nonn

Author

Davide Rotondo, Sep 26 2021

Status

approved