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A085313
Number of distinct 10th power residues modulo n.
12
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, 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, 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
OFFSET
1,2
COMMENTS
This sequence is multiplicative [Li]. - Leon P Smith, Apr 16 2005
LINKS
S. Li, On the number of elements with maximal order in the multiplicative group modulo n, Acta Arithm. 86 (2) (1998) 113, see proof of theorem 2.1
MAPLE
A085313 := proc(m)
{seq( modp(b^10, m), b=0..m-1) };
nops(%) ;
end proc:
seq(A085313(m), m=1..100) ; # R. J. Mathar, Sep 22 2017
MATHEMATICA
a[n_] := Table[PowerMod[i, 10, n], {i, 0, n - 1}] // Union // Length;
Array[a, 100] (* Jean-François Alcover, Mar 25 2020 *)
PROG
(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
CROSSREFS
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.
Sequence in context: A178139 A039642 A027300 * A065458 A341121 A144000
KEYWORD
nonn,mult
AUTHOR
Labos Elemer, Jun 27 2003
STATUS
approved