This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
n = 2: GL(2,2) is isomorphic to S3 which has exponent 6 (see: A003418).
n = 3: The set of element orders of GL(3,2) is {1,2,3,4,7} so the exponent is 84.
n = 5: The set of element orders of GL(5,2) is {1,2,3,4,5, 6,7,8,12,14, 15,21,31} so the exponent is 26040 (see: A053651).
for n in [1..18] do Exponent(GL(n,2)); end for;
with(numtheory):
a:= proc(n) local t; t:= 2^ilog2(n);
`if`(tAlois P. Heinz, Feb 04 2013
f[q_, n_] := With[{p = Sort[Divisors[q]][[2]]},
p^Ceiling[Log[p, n]] Product[Cyclotomic[k, q], {k, n}]]; f[2,#]&/@Range[100]
a(n) = 2^ceil(log(n)/log(2))*prod(k=1, n, polcyclo(k, 2)); \\ Michel Marcus, Jan 29 2020
nmax = 40; CoefficientList[Series[Product[1/(1 - x^k/(1 - x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 22 2019 *)
N=66; x='x+O('x^N); Vec(1/prod(k=1, N, 1-x^k/(1-x^(2*k))))
The a(1) = 1 through a(7) = 14 compositions:
(1) (1) (1) (1) (1) (1) (1)
(2) (3) (2) (5) (2) (7)
(1,2) (4) (1,4) (3) (1,6)
(2,1) (1,3) (2,3) (6) (2,5)
(3,1) (3,2) (1,2) (3,4)
(4,1) (1,5) (4,3)
(2,1) (5,2)
(2,4) (6,1)
(4,2) (1,2,4)
(5,1) (1,4,2)
(1,2,3) (2,1,4)
(1,3,2) (2,4,1)
(2,1,3) (4,1,2)
(2,3,1) (4,2,1)
(3,1,2)
(3,2,1)
Table[Sum[Length[Join@@Permutations/@Select[IntegerPartitions[d],UnsameQ@@#&]],{d,Divisors[n]}],{n,12}]
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