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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

Cf. A333570, A334006, A337632.

Sequence in context: A001917 A240545 A091591 * A227796 A109374 A079706

Adjacent sequences:  A337630 A337631 A337632 * A337634 A337635 A337636

KEYWORD

nonn,tabl

AUTHOR

Peter Kagey, Sep 12 2020

STATUS

approved

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Last modified February 26 17:22 EST 2021. Contains 341632 sequences. (Running on oeis4.)