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.
Original entry on oeis.org
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, 18, 36, 216, 280, 288, 156, 16, 6, 16, 144, 160, 1240, 720, 1512, 320, 48, 4, 30, 96, 432, 1120, 5040, 5580, 4096, 1008, 60, 10, 16, 216, 640, 5400, 6048, 31992, 14976, 15552, 2640, 176
Offset: 1
Array begins:
n\k| 2 3 4 5 6 7 8 9 ...
---+---------------------------------------------------
1 | 1 1 2 2 4 2 6 4 ...
2 | 1 2 4 4 12 8 18 16 ...
3 | 2 4 12 20 56 36 144 96 ...
4 | 2 8 32 48 216 160 432 640 ...
5 | 6 22 120 280 1240 1120 5400 5280 ...
6 | 6 48 288 720 5040 6048 23328 27648 ...
7 | 18 156 1512 5580 31992 37856 254016 340704 ...
8 | 16 320 4096 14976 139968 192000 829440 1966080 ...
...
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A369291[n_, k_] := EulerPhi[k^n - 1]/n;
Table[A369291[k, n-k+2], {n, 15}, {k, n}] (* Paolo Xausa, Jun 17 2024 *)
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T(n,k) = eulerphi(k^n-1)/n
A295496
a(n) = phi(6^n-1)/n, where phi is Euler's totient function (A000010).
Original entry on oeis.org
4, 12, 56, 216, 1240, 5040, 31992, 139968, 828576, 3720000, 25238048, 104509440, 803499840, 3687014016, 24373440000, 110630707200, 790546192128, 3463116249600, 25522921047520, 108957312000000, 816244048599840, 3924124012353600, 26682733370563200
Offset: 1
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Array[EulerPhi[6^# - 1]/# &, 25] (* Paolo Xausa, Jun 17 2024 *)
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{a(n) = eulerphi(6^n-1)/n}
A295497
a(n) = phi(10^n-1)/n, where phi is Euler's totient function (A000010).
Original entry on oeis.org
6, 30, 216, 1500, 12960, 77760, 948192, 7344000, 72071856, 589032000, 6060314304, 38491200000, 496775732544, 4309959326400, 40676940288000, 345599944704000, 3921566733817776, 24555273410096640, 350877192982456140, 2915072245440000000
Offset: 1
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Array[EulerPhi[10^# - 1]/# &, 25] (* Paolo Xausa, Jun 17 2024 *)
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{a(n) = eulerphi(10^n-1)/n}
A158502
Array T(n,k) read by antidiagonals: number of primitive polynomials of degree k over GF(prime(n)).
Original entry on oeis.org
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
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
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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:
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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 *)
Showing 1-4 of 4 results.
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