A085310 Number of distinct 7th 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, 23, 15, 21, 26, 19, 21, 5, 30, 31, 17, 33, 34, 35, 21, 37, 38, 39, 25, 41, 42, 7, 33, 35, 46, 47, 27, 7, 42, 51, 39, 53, 38, 55, 35, 57, 10, 59, 45, 61, 62, 49, 33, 65, 66, 67, 51, 69, 70, 11, 35, 73, 74

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

A085310 := proc(m)
    {seq( modp(b^7, m), b=0..m-1) };
    nops(%) ;
end proc:
seq(A085310(m), m=1..100) ; # R. J. Mathar, Sep 22 2017

Mathematica

a[n_] := Table[PowerMod[i, 7, n], {i, 0, n - 1}] // Union // Length;
Array[a, 100] (* Jean-François Alcover, Mar 24 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^7%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], A085311[k=8], A085312[k=9], A085313[k=10], A085314[k=11], A228849[k=12], A055653.

Sequence in context: A353842 A353832 A085314 * A055653 A155918 A344705

Adjacent sequences: A085307 A085308 A085309 * A085311 A085312 A085313

Keyword

nonn,mult

Author

Labos Elemer, Jun 27 2003

Status

approved