A195637 revision #19
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A195637
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Number of distinct residues of k^n (mod n), k=0..n-1.
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23
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1, 2, 3, 2, 5, 4, 7, 2, 3, 6, 11, 4, 13, 8, 15, 2, 17, 4, 19, 4, 9, 12, 23, 4, 5, 14, 3, 8, 29, 12, 31, 2, 33, 18, 35, 4, 37, 20, 15, 4, 41, 8, 43, 12, 15, 24, 47, 4, 7, 6, 51, 8, 53, 4, 15, 8, 21, 30, 59, 8, 61, 32, 9, 2, 65, 24, 67, 10, 69, 24, 71, 4, 73
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OFFSET
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1,2
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COMMENTS
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a(n) = n if n prime.
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LINKS
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EXAMPLE
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a(18) = 4 because k^18 == 0, 1, 9, 10 (mod 18) => 4 distinct residues.
The triangle of k^n (mod n) starts in row n=1 with columns k>=0 as:
0;
0, 1;
0, 1, 2;
0, 1, 0, 1;
0, 1, 2, 3, 4;
0, 1, 4, 3, 4, 1;
0, 1, 2, 3, 4, 5, 6;
0, 1, 0, 1, 0, 1, 0, 1;
0, 1, 8, 0, 1, 8, 0, 1, 8;
0, 1, 4, 9, 6, 5, 6, 9, 4, 1;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10;
0, 1, 4, 9, 4, 1, 0, 1, 4, 9, 4, 1;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12;
Its row sums are 0, 1, 3, 2, 10, 13, 21, 4, 27, 45, 55, 38, 78, 77, 105, 8,.... (End)
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MAPLE
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a:= n-> nops ({seq (k&^n mod n, k=0..n-1)}):
seq (a(n), n=1..100);
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MATHEMATICA
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Table[Length[Union[PowerMod[Range[0, n - 1], n, n]]], {n, 100}] (* T. D. Noe, Sep 21 2011 *)
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PROG
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(Python)
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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editing
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