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

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, 18, 6, 48, 240, 960, 1120, 720, 156, 16, 10, 48, 816, 1536, 12880, 6048, 5580, 320, 48, 12, 80, 756, 5376, 24752, 62208, 37856, 14976, 1008, 60, 8, 96, 1560, 8640, 141984, 224640, 1087632, 192000, 99360

Offset: 1

Author

R. J. Mathar, Aug 29 2011

Keywords

• nonn
• tabl
• easy

Examples

			The array starts in row n=1 with columns k>=1 as
1, 1,  2,     2,     6,      6,     18,     16,      48,       60,  A011260
1, 2,  4,     8,    22,     48,    156,    320,    1008,     2640,  A027385
2, 4,  20,   48,   280,    720,   5580,  14976,   99360,   291200,  A027741
2, 8,  36,  160,  1120,   6048,  37856, 192000, 1376352,  8512000,  A027743
4,16, 144,  960, 12880,  62208,1087632,7027200,85098816,691398400,  A319166
4,24, 240, 1536, 24752, 224640,2988024,21934080
		

Links

• Vincenzo Librandi, Rows n = 1..50, flattened

Crossrefs

Cf. A000010, A000040.

Programs

Maple

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:

Mathematica

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 *)

Formula

T(n,k) = A000010(p^k-1)/k = A369291(k, p) with p=A000040(n).