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A085314 Number of distinct 11th powers modulo n.

%I A085314 #23 Mar 25 2020 06:03:27
%S A085314 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,
%T A085314 21,29,30,31,17,33,34,35,21,37,38,39,25,41,42,43,33,35,6,47,27,43,42,
%U A085314 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
%N A085314 Number of distinct 11th powers modulo n.
%C A085314 Compare with enigmatic similarity of this and analogous odd-th power counts to A055653.
%C A085314 This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
%H A085314 T. D. Noe, <a href="/A085314/b085314.txt">Table of n, a(n) for n = 1..1000</a>
%H A085314 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 A085314 A085314 := proc(m)
%p A085314     {seq( modp(b^11,m),b=0..m-1) };
%p A085314     nops(%) ;
%p A085314 end proc:
%p A085314 seq(A085314(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017
%t A085314 a[n_] := Table[PowerMod[i, 11, n], {i, 0, n - 1}] // Union // Length;
%t A085314 Array[a, 100] (* _Jean-François Alcover_, Mar 25 2020 *)
%o A085314 (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
%Y A085314 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.
%K A085314 nonn,mult
%O A085314 1,2
%A A085314 _Labos Elemer_, Jun 27 2003