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

1,4

Links

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

Formula

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

Example

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,
4,24, 240, 1536, 24752, 224640,2988024,21934080

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 *)

Crossrefs

Cf. A000010, A000040.

Sequence in context: A369291 A074912 A274207 * A331813 A215244 A195427

Adjacent sequences: A158499 A158500 A158501 * A158503 A158504 A158505

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Aug 29 2011

Status

approved