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

Author

Arkadiusz Wesolowski, Sep 05 2013

Keywords

• nonn
• mult

Links

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

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).

Programs

Magma

[#Set([k^12 mod n : k in [1..n]]) : n in [1..81]];

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 *)

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