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A085314
Number of distinct 11th powers modulo n.
12
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, 21, 29, 30, 31, 17, 33, 34, 35, 21, 37, 38, 39, 25, 41, 42, 43, 33, 35, 6, 47, 27, 43, 42, 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
OFFSET
1,2
COMMENTS
Compare with enigmatic similarity of this and analogous odd-th power counts to A055653.
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
A085314 := proc(m)
{seq( modp(b^11, m), b=0..m-1) };
nops(%) ;
end proc:
seq(A085314(m), m=1..100) ; # R. J. Mathar, Sep 22 2017
MATHEMATICA
a[n_] := Table[PowerMod[i, 11, 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^11%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], A085313[k=10], A228849[k=12], A055653.
Sequence in context: A052274 A353842 A353832 * A085310 A055653 A155918
KEYWORD
nonn,mult
AUTHOR
Labos Elemer, Jun 27 2003
STATUS
approved