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 A085311 Number of distinct 8th powers modulo n. 13
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is multiplicative. - Leon P Smith, Apr 16 2005 LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 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 R. J. Mathar, Size of the set of residues of integer powers of fixed exponent, (2017). MAPLE A085311 := proc(m)     {seq( modp(b^8, m), b=0..m-1) };     nops(%) ; end proc: seq(A085311(m), m=1..100) ; # R. J. Mathar, Sep 22 2017 MATHEMATICA a[n_] := Table[PowerMod[i, 8, n], {i, 0, n - 1}] // Union // Length; Array[a, 100] (* Jean-François Alcover, Mar 24 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^8%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], A085312[k=9], A085313[k=10], A085314[k=11], A228849[k=12], A055653. Sequence in context: A023161 A023155 A277847 * A052273 A074912 A274207 Adjacent sequences:  A085308 A085309 A085310 * A085312 A085313 A085314 KEYWORD nonn,mult AUTHOR Labos Elemer, Jun 27 2003 STATUS approved

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Last modified January 20 13:06 EST 2022. Contains 350472 sequences. (Running on oeis4.)