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A197929 Number of distinct residues of x^(n-1) (mod n), x=0..n-1. 4
1, 2, 2, 3, 2, 6, 2, 5, 4, 10, 2, 9, 2, 14, 6, 9, 2, 14, 2, 15, 8, 22, 2, 15, 6, 26, 10, 9, 2, 30, 2, 17, 12, 34, 12, 21, 2, 38, 14, 25, 2, 42, 2, 33, 8, 46, 2, 27, 8, 42, 18, 15, 2, 38, 18, 35, 20, 58, 2, 45, 2, 62, 16, 33, 8, 18, 2, 51, 24, 30, 2, 35, 2, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 2 if n prime because the residues are 0 and 1 (Fermat's little theorem).

a(n) = n if n = 2p,  p prime > 2. But there exists nonprime numbers q such that a(2q) = 2q, for example q = 1, 15, 21, 39,...

LINKS

Table of n, a(n) for n=1..74.

EXAMPLE

a(8) = 5 because x^7 == 0, 1, 3, 5, 7  (mod 8) => 5 distinct residues.

MATHEMATICA

Length[Union[#]]& /@ Table[Mod[k^(n-1), n], {n, 74}, {k, n}]

CROSSREFS

Cf. A000224, A195637.

Sequence in context: A108499 A260895 A107753 * A326849 A328706 A240090

Adjacent sequences:  A197926 A197927 A197928 * A197930 A197931 A197932

KEYWORD

nonn

AUTHOR

Michel Lagneau, Oct 19 2011

STATUS

approved

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Last modified May 25 08:37 EDT 2020. Contains 334587 sequences. (Running on oeis4.)