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%I #21 Sep 08 2022 08:46:25
%S 1,1,2,1,1,2,1,2,2,1,1,1,2,3,2,1,2,4,2,4,2,1,1,2,1,4,1,2,1,2,2,1,2,1,
%T 2,1,1,1,2,1,4,1,2,1,2,1,2,4,6,4,2,4,6,4,2,1,1,2,1,2,1,6,1,2,1,2,1,2,
%U 4,1,4,1,4,1,4,1,4,1,1,1,2,3,4,1,2,7,2
%N 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.
%H Peter Kagey, <a href="/A337633/b337633.txt">Table of n, a(n) for n = 1..10011</a> (first 141 rows, flattened)
%F T(n,k) = A337632(n,k)/A334006(n,k).
%e Triangle begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9
%e ---+-----------------------------
%e 1 | 1;
%e 2 | 1, 2;
%e 3 | 1, 1, 2;
%e 4 | 1, 2, 2, 1;
%e 5 | 1, 1, 2, 3, 2;
%e 6 | 1, 2, 4, 2, 4, 2;
%e 7 | 1, 1, 2, 1, 4, 1, 2;
%e 8 | 1, 2, 2, 1, 2, 1, 2, 1;
%e 9 | 1, 1, 2, 1, 4, 1, 2, 1, 2;
%e 10 | 1, 2, 4, 6, 4, 2, 4, 6, 4, 2;
%e ...
%e T(10, 2) = 4 because
%e 0^2 + 0 == 0 (mod 10),
%e 4^2 + 4 == 0 (mod 10),
%e 5^2 + 5 == 0 (mod 10), and
%e 9^2 + 9 == 0 (mod 10).
%o (Haskell)
%o a337633t n k = length $ filter (\m -> (m^k + m) `mod` n == 0) [0..n-1]
%o (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
%Y Cf. A333570, A334006, A337632.
%K nonn,tabl
%O 1,3
%A _Peter Kagey_, Sep 12 2020
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