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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080738 Array read by rows in which 0th 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-Fran├žois 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 | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 3 08:48 EST 2016. Contains 278698 sequences.