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A337633 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. 3
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, 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, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 1, 1, 2, 3, 4, 1, 2, 7, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 rows, flattened)
FORMULA
T(n,k) = A337632(n,k)/A334006(n,k).
EXAMPLE
Triangle begins:
n\k| 0 1 2 3 4 5 6 7 8 9
---+-----------------------------
1 | 1;
2 | 1, 2;
3 | 1, 1, 2;
4 | 1, 2, 2, 1;
5 | 1, 1, 2, 3, 2;
6 | 1, 2, 4, 2, 4, 2;
7 | 1, 1, 2, 1, 4, 1, 2;
8 | 1, 2, 2, 1, 2, 1, 2, 1;
9 | 1, 1, 2, 1, 4, 1, 2, 1, 2;
10 | 1, 2, 4, 6, 4, 2, 4, 6, 4, 2;
...
T(10, 2) = 4 because
0^2 + 0 == 0 (mod 10),
4^2 + 4 == 0 (mod 10),
5^2 + 5 == 0 (mod 10), and
9^2 + 9 == 0 (mod 10).
PROG
(Haskell)
a337633t n k = length $ filter (\m -> (m^k + m) `mod` n == 0) [0..n-1]
(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
CROSSREFS
Sequence in context: A001917 A240545 A091591 * A358492 A227796 A109374
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Sep 12 2020
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)