|
| |
|
|
A080738
|
|
Array read by rows in which 0-th row is {1,2}; for n>0, n-th row gives finite orders of 2n X 2n integer matrices that are not orders of 2n-1 X 2n-1 integer matrices.
|
|
6
|
|
|
|
1, 2, 3, 4, 6, 5, 8, 10, 12, 7, 9, 14, 15, 18, 20, 24, 30, 16, 21, 28, 36, 40, 42, 60, 11, 22, 35, 45, 48, 56, 70, 72, 84, 90, 120, 13, 26, 33, 44, 63, 66, 80, 105, 126, 140, 168, 180, 210, 39, 52, 55, 78, 88, 110, 112, 132, 144, 240, 252, 280, 360, 420, 17, 32, 34, 65, 77
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
A080739 gives number of elements in n-th row.
|
|
|
REFERENCES
|
J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.
|
|
|
LINKS
|
_Reinhard Zumkeller_, Rows n = 0..25 of triangle, flattened
|
|
|
FORMULA
|
Set of finite orders of n X n integer matrices = {m : A080737(m) <= n}.
|
|
|
EXAMPLE
|
1,2; 3,4,6; 5,8,10,12; 7,9,14,15,18,20,24,30; ...
|
|
|
MATHEMATICA
|
a080737[1] = a080737[2] = 0; a080737[p_?PrimeQ] := a080737[p] = p-1; a080737[n_] := a080737[n] = If[ Length[fi = FactorInteger[n]] == 1, EulerPhi[n], Total[ a080737 /@ (fi[[All, 1]]^fi[[All, 2]])]]; orders = Table[{n, a080737[n]}, {n, 1, 420}]; row[0] = {1, 2}; row[n_] := Select[ orders, 2n-1 <= #[[2]] <= 2n & ][[All, 1]]; A080738 = Flatten[ Table[ row[n], {n, 0, 8}]] (* Jean-François Alcover, Jun 20 2012 *)
|
|
|
PROG
|
(Haskell)
import Data.Map (singleton, deleteFindMin, insertWith)
a080738 n k = a080738_tabf !! n !! k
a080738_row n = a080738_tabf !! n
a080738_tabf = f 3 (drop 2 a080737_list) 3 (singleton 0 [2, 1]) where
f i xs'@(x:xs) till m
| i > till = (reverse row) : f i xs' (3 * head row) m'
| otherwise = f (i + 1) xs till (insertWith (++) (div x 2) [i] m)
where ((_, row), m') = deleteFindMin m
-- Reinhard Zumkeller, Jun 13 2012
|
|
|
CROSSREFS
|
Cf. A080737, A080739-A080742.
Sequence in context: A194507 A118316 A197756 * A032447 A224531 A058213
Adjacent sequences: A080735 A080736 A080737 * A080739 A080740 A080741
|
|
|
KEYWORD
|
nonn,tabf,easy,changed
|
|
|
AUTHOR
|
N. J. A. Sloane, Mar 08 2003
|
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic, Mar 09 2003
|
|
|
STATUS
|
approved
|
| |
|
|
