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A228849 Number of distinct 12th powers modulo n.

%I A228849 #17 May 26 2025 23:50:26
%S A228849 1,2,2,2,2,4,2,2,2,4,6,4,2,4,4,2,5,4,4,4,4,12,12,4,6,4,4,4,8,8,6,3,12,
%T A228849 10,4,4,4,8,4,4,11,8,8,12,4,24,24,4,8,12,10,4,14,8,12,4,8,16,30,8,6,
%U A228849 12,4,5,4,24,12,10,24,8,36,4,7,8,12,8,12,8,14,4,10
%N A228849 Number of distinct 12th powers modulo n.
%H A228849 R. J. Mathar, <a href="/A228849/b228849.txt">Table of n, a(n) for n = 1..10000</a>
%p A228849 A228849 := proc(n)
%p A228849     {seq(i^12 mod n, i=0..n-1)} ;
%p A228849     nops(%) ;
%p A228849 end proc: # _R. J. Mathar_, Sep 21 2017
%t A228849 a[n_] := Table[PowerMod[i, 12, n], {i, 0, n - 1}] // Union // Length;
%t A228849 Array[a, 100] (* _Jean-François Alcover_, Mar 24 2020 *)
%o A228849 (Magma) [#Set([k^12 mod n : k in [1..n]]) : n in [1..81]];
%o A228849 (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^12%k), , 8)) \\ _Charles R Greathouse IV_, Sep 05 2013
%Y A228849 Cf. A000224 (squares), A046530 (cubic residues), A052273 (4th powers), A052274 (5th powers), A052275 (6th powers), A085310 (7th powers), A085311 (8th powers), A085312 (9th powers), A085313 (10th powers), A085314 (11th powers).
%K A228849 nonn,mult
%O A228849 1,2
%A A228849 _Arkadiusz Wesolowski_, Sep 05 2013