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A228849
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Number of distinct 12th powers modulo n.
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12
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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, 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, 12, 4, 5, 4, 24, 12, 10, 24, 8, 36, 4, 7, 8, 12, 8, 12, 8, 14, 4, 10
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OFFSET
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1,2
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LINKS
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MAPLE
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{seq(i^12 mod n, i=0..n-1)} ;
nops(%) ;
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MATHEMATICA
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a[n_] := Table[PowerMod[i, 12, n], {i, 0, n - 1}] // Union // Length;
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PROG
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(Magma) [#Set([k^12 mod n : k in [1..n]]) : n in [1..81]]
(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
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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