cp's OEIS Frontend

A085313 Number of distinct 10th power residues modulo n.

%I A085313 #20 Mar 25 2020 06:03:39
%S A085313 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 A085313 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 A085313 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 A085313 Number of distinct 10th power residues modulo n.
%C A085313 This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
%H A085313 T. D. Noe, <a href="/A085313/b085313.txt">Table of n, a(n) for n = 1..1000</a>
%H A085313 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 A085313 := proc(m)
%p A085313     {seq( modp(b^10,m),b=0..m-1) };
%p A085313     nops(%) ;
%p A085313 end proc:
%p A085313 seq(A085313(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017
%t A085313 a[n_] := Table[PowerMod[i, 10, n], {i, 0, n - 1}] // Union // Length;
%t A085313 Array[a, 100] (* _Jean-François Alcover_, Mar 25 2020 *)
%o A085313 (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 A085313 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 A085313 nonn,mult
%O A085313 1,2
%A A085313 _Labos Elemer_, Jun 27 2003