The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A316622 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A316622

Array read by antidiagonals: T(n,k) is the order of the group GL(n,Z_k).
(history; published version)

#13 by Michael De Vlieger at Sat Oct 29 10:52:24 EDT 2022

STATUS

proposed

approved

#12 by Jianing Song at Sat Oct 29 10:32:51 EDT 2022

STATUS

editing

proposed

#11 by Jianing Song at Sat Oct 29 10:29:52 EDT 2022

COMMENTS

For k >= 2, n! divides T(n,k) since the subgroup of GL(n,k) consisting of all permutation matrices is isomorphic to S_n (the n-th symmetric group). Note that a permutation matrix is an orthogonal matrix, hence having determinant +-1. - _Jianing Song_, Oct 29 2022

#10 by Jianing Song at Sat Oct 29 10:24:11 EDT 2022

COMMENTS

For k >= 2, n! divides T(n,k) since the subgroup of GL(n,k) consisting of all permutation matrices is isomorphic to S_n (the n-th symmetric group)

STATUS

approved

editing

#9 by Peter Luschny at Thu Jul 25 16:57:29 EDT 2019

STATUS

proposed

approved

#8 by Jean-François Alcover at Thu Jul 25 13:04:23 EDT 2019

STATUS

editing

proposed

#7 by Jean-François Alcover at Thu Jul 25 13:02:56 EDT 2019

MATHEMATICA

T[_, 1] = T[0, _] = 1; T[n_, k_] := T[n, k] = Module[{f = FactorInteger[k], p, e}, If[Length[f] == 1, {p, e} = f[[1]]; (p^e)^(n^2)* Product[(1 - 1/p^j), {j, 1, n}], Times @@ (T[n, Power @@ #]& /@ f)]];

#6 by Jean-François Alcover at Thu Jul 25 13:01:54 EDT 2019

MATHEMATICA

T[_, 1] = T[0, _] = 1; T[n_, k_] := T[n, k] = Module[{f = FactorInteger[k]}, If[Length[f] == 1, {p, e} = f[[1]]; (p^e)^(n^2)* Product[(1 - 1/p^j), {j, 1, n}], Times @@ (T[n, Power @@ #]& /@ f)]];

Table[T[n - k + 1, k], {n, 0, 8}, {k, n + 1, 1, -1}] // Flatten (* Jean-François Alcover, Jul 25 2019 *)

STATUS

approved

editing

#5 by Susanna Cuyler at Sun Jul 08 20:00:06 EDT 2018

STATUS

proposed

approved

#4 by Andrew Howroyd at Sun Jul 08 17:36:50 EDT 2018

STATUS

editing

proposed