A028668 -id:A028668 - cp's OEIS frontend

A028684 Pseudo Galois numbers for d=22.

1, 462, 108002664, 12244181663697984, 671907296255880840847211520, 17845802448787704188422900898268569763840, 229407835408995110669430829173445733902175228551055278080, 1427334550066488576237160094041582026191840875706260743124583853079375380480

Offset: 0

Olivier Gérard

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..27

Cf. A028668, A028670, A028671, A028672, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028686.

FoldList[ #1*22^#2 (22^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 22^n * Product[22^n - 22^k, {k, 0, n-1}]; Array[a, 8, 0] (* Amiram Eldar, Jul 14 2025 *)

a(n) = 22^n * prod(k = 0, n-1, 22^n - 22^k); \\ Amiram Eldar, Jul 14 2025

a(n) = 22^n * Product_{k=0..n-1} (22^n - 22^k).

a(n) ~ c * 22^(n^2+n), where c = Product_{k>=1} (1 - 1/22^k) = 0.952479533281... . - Amiram Eldar, Jul 14 2025

A028686 Pseudo Galois numbers for d=24.

Original entry on oeis.org

1, 552, 182822400, 34935377382604800, 3845511050527581426155520000, 243818371522804938361462294653739991040000, 8904331592711942612922766177589119660252055149215744000000, 187309027227336950425268745082789353880120643944720523727102076558245888000000

Offset: 0

Olivier Gérard

nonn

Vincenzo Librandi, Table of n, a(n) for n = 0..26

Cf. A028668, A028670, A028671, A028672, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028684.

FoldList[ #1*24^#2 (24^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 24^n * Product[24^n - 24^k, {k, 0, n-1}]; Array[a, 8, 0] (* Amiram Eldar, Jul 14 2025 *)

a(n) = 24^n * prod(k = 0, n-1, 24^n - 24^k); \\ Amiram Eldar, Jul 14 2025

a(n) = 24^n * Product_{k=0..n-1} (24^n - 24^k).

a(n) ~ c * 24^(n^2+n), where c = Product_{k>=1} (1 - 1/24^k) = 0.956597348026... . - Amiram Eldar, Jul 14 2025

A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.

Original entry on oeis.org

1, 12, 2880, 11612160, 758041804800, 794088208701849600, 13319336815141167562752000, 3575164027575627746190393606144000, 15354978274323252140217954794120612413440000, 1055182047088717407398960909148529544369642384916480000, 1160183823755957350394353874696058298158177597536388268425216000000

Offset: 0

Olivier Gérard

nonn

Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xii (but beware typos!).

Vincenzo Librandi, Table of n, a(n) for n = 0..39

Bisections give A144546 and A144547.
Cf. A028668, A028670, A028671, A028672, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028684, A028686.
Cf. A100221.

f:=proc(n,eps) local m,d;
if n mod 2 = 0 then m:=n/2; d:=gcd(4,2^m-eps);
2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;
else m:=(n-1)/2;
2^(m^2)*mul( 4^i-1, i=1..m);
fi; end;
[seq(f(n,+1),n=0..20)]

FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 4^n * Product[4^n - 4^k, {k, 0, n-1}]; Array[a, 10, 0] (* Amiram Eldar, Jul 14 2025 *)

a(n) = 4^n * prod(k = 0, n-1, 4^n - 4^k); \\ Amiram Eldar, Jul 14 2025

a(n) = 4^n * Product_{k=0..n-1} (4^n - 4^k).

a(n) ~ c * 4^(n^2+n), where c = A100221. - Amiram Eldar, Jul 14 2025

Entry revised by N. J. A. Sloane, Dec 30 2008

Duplicate term 1 removed by Amiram Eldar, Jul 14 2025

A028690 Sorted Galois and Pseudo-Galois numbers.

Original entry on oeis.org

1, 2, 6, 12, 20, 24, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 432, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1344, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352

Offset: 1

Olivier Gérard

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A028665, A028667, A028668, ..., A028689, A028691.

Offset changed to 1 by Alois P. Heinz, Nov 07 2018

cp's OEIS Frontend

A028684 Pseudo Galois numbers for d=22.

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A028686 Pseudo Galois numbers for d=24.

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A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.

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A028690 Sorted Galois and Pseudo-Galois numbers.

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