A316586 Array read by antidiagonals: T(n,k) is the number of elements x in SL(2,Z_n) with x^k == I mod n where I is the identity matrix.

1, 1, 1, 1, 4, 1, 1, 3, 2, 1, 1, 4, 9, 8, 1, 1, 1, 8, 9, 2, 1, 1, 6, 1, 32, 21, 8, 1, 1, 1, 18, 1, 32, 27, 2, 1, 1, 4, 1, 24, 25, 32, 57, 16, 1, 1, 3, 8, 1, 42, 1, 44, 33, 2, 1, 1, 4, 9, 32, 1, 108, 1, 160, 99, 8, 1, 1, 1, 2, 9, 32, 1, 114, 1, 56, 63, 2, 1

Offset

1,5

Comments

All columns are multiplicative.

Links

Table of n, a(n) for n=1..78.

Formula

T(n,k) = Sum_{d|k} A316564(n, d).

Conjecture: T(p,p) = p^2 for p prime.

Example

Array begins:
================================================
  n\k | 1  2   3   4   5   6   7   8   9  10
------+-----------------------------------------
    1 | 1  1   1   1   1   1   1   1   1   1 ...
    2 | 1  4   3   4   1   6   1   4   3   4 ...
    3 | 1  2   9   8   1  18   1   8   9   2 ...
    4 | 1  8   9  32   1  24   1  32   9   8 ...
    5 | 1  2  21  32  25  42   1  32  21  50 ...
    6 | 1  8  27  32   1 108   1  32  27   8 ...
    7 | 1  2  57  44   1 114  49 128  57   2 ...
    8 | 1 16  33 160   1 144   1 256  33  16 ...
    9 | 1  2  99  56   1 198   1  56 243   2 ...
   10 | 1  8  63 128  25 252   1 128  63 200 ...
   11 | 1  2 111 112 265 222   1 112 111 530 ...
   12 | 1 16  81 256   1 432   1 256  81  16 ...
   13 | 1  2 183 184   1 366 469 184 183   2 ...
   14 | 1  8 171 176   1 684  49 512 171   8 ...
   15 | 1  4 189 256  25 756   1 256 189 100 ...
   ...

Crossrefs

Cf. A316564, A316584.

Sequence in context: A293882 A016524 A087963 * A274540 A010323 A353647

Adjacent sequences: A316583 A316584 A316585 * A316587 A316588 A316589

Keyword

nonn,tabl,mult

Author

Andrew Howroyd, Jul 07 2018

Status

approved