A085313 Number of distinct 10th power residues modulo n.

1, 2, 2, 2, 3, 4, 4, 2, 4, 6, 2, 4, 7, 8, 6, 3, 9, 8, 10, 6, 8, 4, 12, 4, 3, 14, 10, 8, 15, 12, 4, 5, 4, 18, 12, 8, 19, 20, 14, 6, 5, 16, 22, 4, 12, 24, 24, 6, 22, 6, 18, 14, 27, 20, 6, 8, 20, 30, 30, 12, 7, 8, 16, 9, 21, 8, 34, 18, 24, 24, 8, 8, 37, 38, 6, 20, 8, 28, 40, 9, 28, 10, 42, 16

Offset

1,2

Comments

This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

S. Li, On the number of elements with maximal order in the multiplicative group modulo n, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1

Maple

A085313 := proc(m)
    {seq( modp(b^10, m), b=0..m-1) };
    nops(%) ;
end proc:
seq(A085313(m), m=1..100) ; # R. J. Mathar, Sep 22 2017

Mathematica

a[n_] := Table[PowerMod[i, 10, n], {i, 0, n - 1}] // Union // Length;
Array[a, 100] (* Jean-François Alcover, Mar 25 2020 *)

Prog

(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^10%k), , 8)) \\ Charles R Greathouse IV, Sep 05 2013

Crossrefs

Cf. A000224[k=2], A046530[k=3], A052273[k=4], A052274[k=5], A052275[k=6], A085310[k=7], A085311[k=8], A085312[k=9], A085314[k=11], A228849[k=12], A055653.

Sequence in context: A178139 A039642 A027300 * A065458 A341121 A144000

Adjacent sequences: A085310 A085311 A085312 * A085314 A085315 A085316

Keyword

nonn,mult

Author

Labos Elemer, Jun 27 2003

Status

approved