A085314 Number of distinct 11th powers modulo n.

1, 2, 3, 3, 5, 6, 7, 5, 7, 10, 11, 9, 13, 14, 15, 9, 17, 14, 19, 15, 21, 22, 3, 15, 21, 26, 19, 21, 29, 30, 31, 17, 33, 34, 35, 21, 37, 38, 39, 25, 41, 42, 43, 33, 35, 6, 47, 27, 43, 42, 51, 39, 53, 38, 55, 35, 57, 58, 59, 45, 61, 62, 49, 33, 65, 66, 7, 51, 9, 70, 71, 35, 73, 74, 63

Offset

1,2

Comments

Compare with enigmatic similarity of this and 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

A085314 := proc(m)
    {seq( modp(b^11, m), b=0..m-1) };
    nops(%) ;
end proc:
seq(A085314(m), m=1..100) ; # R. J. Mathar, Sep 22 2017

Mathematica

a[n_] := Table[PowerMod[i, 11, 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^11%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], A085313[k=10], A228849[k=12], A055653.

Sequence in context: A052274 A353842 A353832 * A085310 A055653 A155918

Adjacent sequences: A085311 A085312 A085313 * A085315 A085316 A085317

Keyword

nonn,mult

Author

Labos Elemer, Jun 27 2003

Status

approved