cp's OEIS Frontend

A085311 Number of distinct 8th powers modulo n.

%I A085311 #24 Aug 05 2022 08:01:44
%S A085311 1,2,2,2,2,4,4,2,4,4,6,4,4,8,4,2,3,8,10,4,8,12,12,4,6,8,10,8,8,8,16,2,
%T A085311 12,6,8,8,10,20,8,4,6,16,22,12,8,24,24,4,22,12,6,8,14,20,12,8,20,16,
%U A085311 30,8,16,32,16,3,8,24,34,6,24,16,36,8,10,20,12,20,24,16,40,4,28,12,42,16,6
%N A085311 Number of distinct 8th powers modulo n.
%C A085311 This sequence is multiplicative. - Leon P Smith, Apr 16 2005
%H A085311 T. D. Noe, <a href="/A085311/b085311.txt">Table of n, a(n) for n = 1..1000</a>
%H A085311 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
%H A085311 R. J. Mathar, <a href="/A293482/a293482.pdf">Size of the set of residues of integer powers of fixed exponent</a>, (2017).
%p A085311 A085311 := proc(m)
%p A085311     {seq( modp(b^8,m),b=0..m-1) };
%p A085311     nops(%) ;
%p A085311 end proc:
%p A085311 seq(A085311(m),m=1..100) ; # _R. J. Mathar_, Sep 22 2017
%t A085311 a[n_] := Table[PowerMod[i, 8, n], {i, 0, n - 1}] // Union // Length;
%t A085311 Array[a, 100] (* _Jean-François Alcover_, Mar 24 2020 *)
%o A085311 (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^8%k), , 8)) \\ _Charles R Greathouse IV_, Sep 05 2013
%Y A085311 Cf. A000224[k=2], A046530[k=3], A052273[k=4], A052274[k=5], A052275[k=6], A085310[k=7], A085312[k=9], A085313[k=10], A085314[k=11], A228849[k=12], A055653.
%K A085311 nonn,mult
%O A085311 1,2
%A A085311 _Labos Elemer_, Jun 27 2003