A369291 Array read by antidiagonals: T(n,k) = phi(k^n-1)/n, where phi is Euler's totient function (A000010), n >= 1, k >= 2.

1, 1, 1, 2, 2, 2, 2, 4, 4, 2, 4, 4, 12, 8, 6, 2, 12, 20, 32, 22, 6, 6, 8, 56, 48, 120, 48, 18, 4, 18, 36, 216, 280, 288, 156, 16, 6, 16, 144, 160, 1240, 720, 1512, 320, 48, 4, 30, 96, 432, 1120, 5040, 5580, 4096, 1008, 60, 10, 16, 216, 640, 5400, 6048, 31992, 14976, 15552, 2640, 176

Offset

1,4

Comments

For k a prime power, T(n,k) is the number of primitive polynomials of degree n over GF(k). See A011260, A027385 for additional information.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 antidiagonals)

Eric Weisstein's World of Mathematics, Totient Function.

Wikipedia, Euler's totient function.

Example

Array begins:
n\k|  2   3    4     5      6      7      8       9 ...
---+---------------------------------------------------
 1 |  1   1    2     2      4      2      6       4 ...
 2 |  1   2    4     4     12      8     18      16 ...
 3 |  2   4   12    20     56     36    144      96 ...
 4 |  2   8   32    48    216    160    432     640 ...
 5 |  6  22  120   280   1240   1120   5400    5280 ...
 6 |  6  48  288   720   5040   6048  23328   27648 ...
 7 | 18 156 1512  5580  31992  37856 254016  340704 ...
 8 | 16 320 4096 14976 139968 192000 829440 1966080 ...
  ...

Prog

(PARI) T(n, k) = eulerphi(k^n-1)/n

Crossrefs

Rows n=1..3 and 5 are A000010(k-1), A319210, A319213, A319214.

Columns 2..11 are A011260, A027385, A027695, A027741, A295496, A027743, A027744, A027745, A295497, A319166.

Cf. A319183.

Sequence in context: A277847 A085311 A052273 * A074912 A274207 A158502

Adjacent sequences: A369288 A369289 A369290 * A369292 A369293 A369294

Keyword

nonn,tabl,easy

Author

Andrew Howroyd, Jan 28 2024

Status

approved