A085312 Number of distinct 9th powers modulo n.

1, 2, 3, 3, 5, 6, 3, 5, 3, 10, 11, 9, 5, 6, 15, 9, 17, 6, 3, 15, 9, 22, 23, 15, 21, 10, 3, 9, 29, 30, 11, 17, 33, 34, 15, 9, 5, 6, 15, 25, 41, 18, 15, 33, 15, 46, 47, 27, 15, 42, 51, 15, 53, 6, 55, 15, 9, 58, 59, 45, 21, 22, 9, 33, 25, 66, 23, 51, 69, 30, 71, 15, 9, 10, 63, 9, 33, 30, 27

Offset: 1

Author

Labos Elemer, Jun 27 2003

Keywords

• nonn
• mult

Comments

Compare with enigmatic similarity of analogous odd-th power counts to A055653.

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

Crossrefs

Cf. A000224[k=2], A046530[k=3], A052273[k=4], A052274[k=5], A052275[k=6], A085310[k=7], A085311[k=8], A085313[k=10], A085314[k=11], A228849[k=12], A055653.

Programs

Maple

A085312 := proc(m)
    {seq( modp(b^9,m),b=0..m-1) };
    nops(%) ;
end proc:
seq(A085312(m),m=1..100) ; # R. J. Mathar, Sep 22 2017

Mathematica

a[n_] := Table[PowerMod[i, 9, n], {i, 0, n - 1}] // Union // Length;
Array[a, 100] (* Jean-François Alcover, Mar 25 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^9%k), , 8)) \\ Charles R Greathouse IV, Sep 05 2013