A028683
Pseudo Galois numbers for d=21.
Original entry on oeis.org
1, 420, 81496800, 6988909668048000, 264339188251171547754240000, 4409145118315866486641282521305984000000, 32432910584848683243891703579686352553931989191680000000, 105209765057463921593261518265177017436422522866428383386348592435200000000
Offset: 0
Cf.
A028668,
A028670,
A028671,
A028672,
A028674,
A028676,
A028677,
A028678,
A028680,
A028682,
A028684,
A028686.
-
FoldList[ #1*21^#2 (21^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 21^n * Product[21^n - 21^k, {k, 0, n-1}]; Array[a, 8, 0] (* Amiram Eldar, Jul 14 2025 *)
-
a(n) = 21^n * prod(k = 0, n-1, 21^n - 21^k); \\ 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
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
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
- 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!).
Cf.
A028668,
A028670,
A028671,
A028672,
A028674,
A028676,
A028677,
A028678,
A028680,
A028682,
A028683,
A028684,
A028686.
-
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
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