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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.
13
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.
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 ...
...
MATHEMATICA
A369291[n_, k_] := EulerPhi[k^n - 1]/n;
Table[A369291[k, n-k+2], {n, 15}, {k, n}] (* Paolo Xausa, Jun 17 2024 *)
PROG
(PARI) T(n, k) = eulerphi(k^n-1)/n
CROSSREFS
Rows n=1..3 and 5 are A000010(k-1), A319210, A319213, A319214.
Cf. A319183.
Sequence in context: A277847 A085311 A052273 * A074912 A274207 A158502
KEYWORD
nonn,tabl,easy
AUTHOR
Andrew Howroyd, Jan 28 2024
STATUS
approved