login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A277227 Triangular array T read by rows: T(n,k) gives the additive orders k modulo n, for k = 0,1, ..., n-1. 2
1, 1, 2, 1, 3, 3, 1, 4, 2, 4, 1, 5, 5, 5, 5, 1, 6, 3, 2, 3, 6, 1, 7, 7, 7, 7, 7, 7, 1, 8, 4, 8, 2, 8, 4, 8, 1, 9, 9, 3, 9, 9, 3, 9, 9, 1, 10, 5, 10, 5, 2, 5, 10, 5, 10, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 12, 6, 4, 3, 12, 2, 12, 3, 4, 6, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

As a sequence A054531(n) = a(n+1), n >= 1.

As a triangular array this is the row reversed version of A054531.

The additive order of an element x of a group (G, +) is the least positive integer j with j*x := x + x + ... + x (j summands) = 0.

LINKS

Indranil Ghosh, Rows 1..100 of triangle, flattened

FORMULA

T(n, k) = order of the elements k  of the finite abelian group (Z/(n Z), +), for k = 0, 1, ..., n-1.

T(n, k) = n/GCD(n, k), n >= 1, k = 0, 1, ..., n-1.

T(n, k) = A054531(n, n-k), n >=1, k = 0, 1, ..., n-1.

EXAMPLE

The triangle begins:

n\k 0  1  2  3  4  5  6  7  8  9 10 11 ...

1:  1

2:  1  2

3:  1  3  3

4:  1  4  2  4

5:  1  5  5  5  5

6:  1  6  3  2  3  6

7:  1  7  7  7  7  7  7

8:  1  8  4  8  2  8  4  8

9:  1  9  9  3  9  9  3  9  9

10: 1 10  5 10  5  2  5 10  5 10

11: 1 11 11 11 11 11 11 11 11 11 11

12: 1 12  6  4  3 12  2 12  3  4  6 12

...

T(n, 0) = 1*0 = 0 = 0 (mod n), and n/GCD(n,0) = n/n = 1.

T(4, 2) = 2 because 2 + 2 = 4 = 0 (mod 4) and 2 is not 0 (mod 4).

T(4, 2) = n/GCD(2, 4) = 4/2 = 2.

CROSSREFS

Cf. A054531.

Sequence in context: A049834 A134625 A325477 * A054531 A324602 A319226

Adjacent sequences:  A277224 A277225 A277226 * A277228 A277229 A277230

KEYWORD

nonn,tabl,easy

AUTHOR

Wolfdieter Lang, Oct 20 2016

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 12 19:50 EDT 2021. Contains 342932 sequences. (Running on oeis4.)