A085313 - OEIS

%I #20 Mar 25 2020 06:03:39

%S 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,

%T 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,

%U 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

%N Number of distinct 10th power residues modulo n.

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

%H T. D. Noe, <a href="/A085313/b085313.txt">Table of n, a(n) for n = 1..1000</a>

%H S. Li, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-aav86i2p113bwm">On the number of elements with maximal order in the multiplicative group modulo n</a>, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1

%p A085313 := proc(m)

%p     {seq( modp(b^10,m),b=0..m-1) };

%p     nops(%) ;

%p end proc:

%p seq(A085313(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017

%t a[n_] := Table[PowerMod[i, 10, n], {i, 0, n - 1}] // Union // Length;

%t Array[a, 100] (* _Jean-François Alcover_, Mar 25 2020 *)

%o (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

%Y 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.

%K nonn,mult

%O 1,2

%A _Labos Elemer_, Jun 27 2003