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A337632
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Triangle read by rows: T(n,k) is the number of nonnegative integers m < n such that m^k - m == 0 (mod n), where 0 <= k < n.
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3
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1, 1, 2, 1, 3, 2, 1, 4, 2, 3, 1, 5, 2, 3, 2, 1, 6, 4, 6, 4, 6, 1, 7, 2, 3, 4, 3, 2, 1, 8, 2, 5, 2, 5, 2, 5, 1, 9, 2, 3, 4, 3, 2, 7, 2, 1, 10, 4, 6, 4, 10, 4, 6, 4, 10, 1, 11, 2, 3, 2, 3, 6, 3, 2, 3, 2, 1, 12, 4, 9, 4, 9, 4, 9, 4, 9, 4, 9, 1, 13, 2, 3, 4, 5, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
n\k| 0 1 2 3 4 5 6 7 8 9
---+--------------------------------
1 | 1;
2 | 1, 2;
3 | 1, 3, 2;
4 | 1, 4, 2, 3;
5 | 1, 5, 2, 3, 2;
6 | 1, 6, 4, 6, 4, 6;
7 | 1, 7, 2, 3, 4, 3, 2;
8 | 1, 8, 2, 5, 2, 5, 2, 5;
9 | 1, 9, 2, 3, 4, 3, 2, 7, 2;
10 | 1, 10, 4, 6, 4, 10, 4, 6, 4, 10;
...
T(10,2) = 4 because
0^2 - 0 == 0 (mod 10),
1^2 - 1 == 0 (mod 10),
5^2 - 5 == 0 (mod 10), and
6^2 - 6 == 0 (mod 10).
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PROG
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(Haskell)
a337632t n k = length $ filter (\m -> (m^k - m) `mod` n == 0) [0..n-1]
(PARI) T(n, k) = sum(m=0, n-1, Mod(m, n)^k == Mod(m, n)); \\ Michel Marcus, Sep 13 2020
(Magma) [[#[m: m in [0..n-1] | m^k mod n eq m]: k in [0..n-1]]: n in [1..17]]; // Juri-Stepan Gerasimov, Oct 12 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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