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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.

%I A369291 #11 Jun 17 2024 11:04:49
%S A369291 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 A369291 18,36,216,280,288,156,16,6,16,144,160,1240,720,1512,320,48,4,30,96,
%U A369291 432,1120,5040,5580,4096,1008,60,10,16,216,640,5400,6048,31992,14976,15552,2640,176
%N 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.
%C A369291 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 A369291 Andrew Howroyd, <a href="/A369291/b369291.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals)
%H A369291 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%H A369291 Wikipedia, <a href="https://en.wikipedia.org/wiki/Euler%27s_totient_function">Euler's totient function</a>.
%e A369291 Array begins:
%e A369291 n\k|  2   3    4     5      6      7      8       9 ...
%e A369291 ---+---------------------------------------------------
%e A369291  1 |  1   1    2     2      4      2      6       4 ...
%e A369291  2 |  1   2    4     4     12      8     18      16 ...
%e A369291  3 |  2   4   12    20     56     36    144      96 ...
%e A369291  4 |  2   8   32    48    216    160    432     640 ...
%e A369291  5 |  6  22  120   280   1240   1120   5400    5280 ...
%e A369291  6 |  6  48  288   720   5040   6048  23328   27648 ...
%e A369291  7 | 18 156 1512  5580  31992  37856 254016  340704 ...
%e A369291  8 | 16 320 4096 14976 139968 192000 829440 1966080 ...
%e A369291   ...
%t A369291 A369291[n_, k_] := EulerPhi[k^n - 1]/n;
%t A369291 Table[A369291[k, n-k+2], {n, 15}, {k, n}] (* _Paolo Xausa_, Jun 17 2024 *)
%o A369291 (PARI) T(n,k) = eulerphi(k^n-1)/n
%Y A369291 Rows n=1..3 and 5 are A000010(k-1), A319210, A319213, A319214.
%Y A369291 Columns 2..11 are A011260, A027385, A027695, A027741, A295496, A027743, A027744, A027745, A295497, A319166.
%Y A369291 Cf. A319183.
%K A369291 nonn,tabl,easy
%O A369291 1,4
%A A369291 _Andrew Howroyd_, Jan 28 2024