login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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,look

AUTHOR

N. J. A. Sloane, Mar 08 2003

EXTENSIONS

More terms from Vladeta Jovovic, Mar 09 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 18 22:55 EST 2014. Contains 252174 sequences.