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

1,2

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

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 *)

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^9%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], A085313[k=10], A085314[k=11], A228849[k=12], A055653.

Sequence in context: A185026 A289630 A023160 * A046530 A003558 A216066

Adjacent sequences: A085309 A085310 A085311 * A085313 A085314 A085315

Keyword

nonn,mult

Author

Labos Elemer, Jun 27 2003

Status

approved