A228849 Number of distinct 12th powers modulo n.

1, 2, 2, 2, 2, 4, 2, 2, 2, 4, 6, 4, 2, 4, 4, 2, 5, 4, 4, 4, 4, 12, 12, 4, 6, 4, 4, 4, 8, 8, 6, 3, 12, 10, 4, 4, 4, 8, 4, 4, 11, 8, 8, 12, 4, 24, 24, 4, 8, 12, 10, 4, 14, 8, 12, 4, 8, 16, 30, 8, 6, 12, 4, 5, 4, 24, 12, 10, 24, 8, 36, 4, 7, 8, 12, 8, 12, 8, 14, 4, 10

Offset

1,2

Links

R. J. Mathar, Table of n, a(n) for n = 1..10000

Maple

A228849 := proc(n)
    {seq(i^12 mod n, i=0..n-1)} ;
    nops(%) ;
end proc: # R. J. Mathar, Sep 21 2017

Mathematica

a[n_] := Table[PowerMod[i, 12, n], {i, 0, n - 1}] // Union // Length;
Array[a, 100] (* Jean-François Alcover, Mar 24 2020 *)

Prog

(Magma) [#Set([k^12 mod n : k in [1..n]]) : n in [1..81]]
(PARI) a(n)=my(f=factor(n)); prod(i=1, #f[, 1], my(k=f[i, 1]^f[i, 2]); #vecsort(vector(k, i, i^12%k), , 8)) \\ Charles R Greathouse IV, Sep 05 2013

Crossrefs

Cf. A000224 (squares), A046530 (cubic residues), A052273 (4th powers), A052274 (5th powers), A052275 (6th powers), A085310 (7th powers), A085311 (8th powers), A085312 (9th powers), A085313 (10th powers), A085314 (11th powers).

Sequence in context: A127973 A300654 A023157 * A359541 A069733 A187467

Adjacent sequences: A228846 A228847 A228848 * A228850 A228851 A228852

Keyword

nonn,mult

Author

Arkadiusz Wesolowski, Sep 05 2013

Status

approved