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A202034 Number of distinct prime residues of k^n (mod n), k=0..n-1. 4
0, 0, 1, 0, 2, 1, 3, 0, 0, 1, 4, 0, 5, 3, 6, 0, 6, 0, 7, 1, 2, 3, 8, 0, 1, 4, 0, 0, 9, 1, 10, 0, 11, 4, 11, 0, 11, 6, 3, 0, 12, 1, 13, 2, 3, 7, 14, 0, 2, 0, 15, 2, 15, 0, 3, 0, 5, 6, 16, 0, 17, 8, 0, 0, 18, 3, 18, 2, 19, 2, 19, 0, 20, 10, 2, 4, 21, 1, 21, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

If n is a prime number, a(n) = A000720(n) - 1 because the number of distinct residues of k^n (mod n) = n.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(7) = 3  because  k^7 == 0, 1, 2, 3, 4, 5, 6 (mod 7) including 3 prime residues  2, 3, 5.

MAPLE

for n from 1 to 100 do: W:={}:for k from 0 to n-1 do:z:= irem(k^n, n): if type(z, prime)=true then W:=W union {z}:else fi:od: x:=nops(W): printf(`%d, `, x): od:

MATHEMATICA

Table[Length[Select[Union[Table[Mod[k^n, n], {k, 0, n - 1}]], PrimeQ]], {n, 81}] (* Alonso del Arte, Dec 10 2011 *)

Count[Union[#], _?PrimeQ]&/@Table[PowerMod[k, n, n], {n, 100}, {k, 0, n-1}] (* Harvey P. Dale, Sep 24 2022 *)

CROSSREFS

Cf. A000720, A132213, A195637.

Sequence in context: A177438 A002431 A259328 * A323881 A062963 A143255

Adjacent sequences:  A202031 A202032 A202033 * A202035 A202036 A202037

KEYWORD

nonn,changed

AUTHOR

Michel Lagneau, Dec 09 2011

STATUS

approved

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Last modified October 4 21:22 EDT 2022. Contains 357240 sequences. (Running on oeis4.)