%I #11 Jun 17 2024 11:04:49

%S 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,

%T 18,36,216,280,288,156,16,6,16,144,160,1240,720,1512,320,48,4,30,96,

%U 432,1120,5040,5580,4096,1008,60,10,16,216,640,5400,6048,31992,14976,15552,2640,176

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

%C 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.

%H Andrew Howroyd, <a href="/A369291/b369291.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.

%e Array begins:

%e n\k| 2 3 4 5 6 7 8 9 ...

%e ---+---------------------------------------------------

%e 1 | 1 1 2 2 4 2 6 4 ...

%e 2 | 1 2 4 4 12 8 18 16 ...

%e 3 | 2 4 12 20 56 36 144 96 ...

%e 4 | 2 8 32 48 216 160 432 640 ...

%e 5 | 6 22 120 280 1240 1120 5400 5280 ...

%e 6 | 6 48 288 720 5040 6048 23328 27648 ...

%e 7 | 18 156 1512 5580 31992 37856 254016 340704 ...

%e 8 | 16 320 4096 14976 139968 192000 829440 1966080 ...

%e ...

%t A369291[n_, k_] := EulerPhi[k^n - 1]/n;

%t Table[A369291[k, n-k+2], {n, 15}, {k, n}] (* _Paolo Xausa_, Jun 17 2024 *)

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

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

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

%Y Cf. A319183.

%K nonn,tabl,easy

%O 1,4

%A _Andrew Howroyd_, Jan 28 2024