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A085312 Number of distinct 9th powers modulo n.

%I A085312 #20 Mar 25 2020 06:03:50
%S A085312 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,
%T A085312 30,11,17,33,34,15,9,5,6,15,25,41,18,15,33,15,46,47,27,15,42,51,15,53,
%U A085312 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
%N A085312 Number of distinct 9th powers modulo n.
%C A085312 Compare with enigmatic similarity of analogous odd-th power counts to A055653.
%C A085312 This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
%H A085312 T. D. Noe, <a href="/A085312/b085312.txt">Table of n, a(n) for n = 1..1000</a>
%H A085312 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 A085312 A085312 := proc(m)
%p A085312     {seq( modp(b^9,m),b=0..m-1) };
%p A085312     nops(%) ;
%p A085312 end proc:
%p A085312 seq(A085312(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017
%t A085312 a[n_] := Table[PowerMod[i, 9, n], {i, 0, n - 1}] // Union // Length;
%t A085312 Array[a, 100] (* _Jean-François Alcover_, Mar 25 2020 *)
%o A085312 (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
%Y A085312 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.
%K A085312 nonn,mult
%O A085312 1,2
%A A085312 _Labos Elemer_, Jun 27 2003