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A158502 Array T(n,k) read by antidiagonals: number of primitive polynomials of degree k over GF(prime(n)).

%I A158502 #28 Nov 08 2024 11:38:33
%S A158502 1,1,1,2,2,2,2,4,4,2,4,8,20,8,6,4,16,36,48,22,6,8,24,144,160,280,48,
%T A158502 18,6,48,240,960,1120,720,156,16,10,48,816,1536,12880,6048,5580,320,
%U A158502 48,12,80,756,5376,24752,62208,37856,14976,1008,60,8,96,1560,8640,141984,224640,1087632,192000,99360
%N A158502 Array T(n,k) read by antidiagonals: number of primitive polynomials of degree k over GF(prime(n)).
%H A158502 Vincenzo Librandi, <a href="/A158502/b158502.txt">Rows n = 1..50, flattened</a>
%F A158502 T(n,k) = A000010(p^k-1)/k = A369291(k, p) with p=A000040(n).
%e A158502 The array starts in row n=1 with columns k>=1 as
%e A158502 1, 1,  2,     2,     6,      6,     18,     16,      48,       60,  A011260
%e A158502 1, 2,  4,     8,    22,     48,    156,    320,    1008,     2640,  A027385
%e A158502 2, 4,  20,   48,   280,    720,   5580,  14976,   99360,   291200,  A027741
%e A158502 2, 8,  36,  160,  1120,   6048,  37856, 192000, 1376352,  8512000,  A027743
%e A158502 4,16, 144,  960, 12880,  62208,1087632,7027200,85098816,691398400,  A319166
%e A158502 4,24, 240, 1536, 24752, 224640,2988024,21934080
%p A158502 A := proc(n,k) local p ; p := ithprime(n) ; if k = 0 then 1; else numtheory[phi](p^k-1)/k ; end if;end proc:
%t A158502 t[n_, k_] := If[k == 0, 1, p = Prime[n]; EulerPhi[p^k - 1]/k]; Flatten[ Table[t[n - k + 1, k], {n, 1, 11}, {k, 1, n}]] (* _Jean-François Alcover_, Jun 04 2012, after Maple *)
%Y A158502 Cf. A000010, A000040.
%K A158502 nonn,tabl,easy
%O A158502 1,4
%A A158502 _R. J. Mathar_, Aug 29 2011