login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132442 Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093(transform). 3
1, 1, 3, 1, 1, 4, 1, 3, 1, 7, 1, 1, 1, 1, 6, 1, 3, 4, 3, 1, 12, 1, 1, 1, 1, 1, 1, 8, 1, 3, 1, 7, 1, 3, 1, 15, 1, 1, 4, 1, 1, 4, 1, 1, 13, 1, 3, 1, 3, 6, 3, 1, 3, 1, 18, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 1, 3, 4, 7, 1, 12, 1, 7, 4, 3, 1, 28, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 14, 1, 3, 1, 3, 1, 3, 8, 3, 1, 3, 1, 3, 1, 24 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Right border = sigma(n), A000203.

Row sums = A038040.

The function T(n,k) = T(k,n) is defined for k > n, but only the values of k in 1..n as a triangular array are listed here.

LINKS

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

FORMULA

Given an array formed by A051731 * A127093(transform), extract the first n terms of row n to form the triangle.

T(n,k) = A000203(gcd(n,k)). - Reinhard Zumkeller, Dec 12 2015

EXAMPLE

First few rows of the array:

  1,  1,  1,  1,  1,  1,  1, ...

  1,  3,  1,  3,  1,  3,  1, ...

  1,  1,  4,  1,  1,  4,  1, ...

  1,  3,  1,  7,  1,  3,  1, ...

  1,  1,  1,  1,  6,  1,  1, ...

  1,  3,  4,  3,  1, 12,  1, ...

  ...

First few rows of the triangle:

  1;

  1,  3;

  1,  1,  4;

  1,  3,  1,  7;

  1,  1,  1,  1,  6;

  1,  3,  4,  3,  1, 12;

  1,  1,  1,  1,  1,  1,  8;

  1,  3,  1,  7,  1,  3,  1, 15;

  ...

MATHEMATICA

T[ n_, k_] := If[ n < 1 || k < 1, 0, If[ k > n, T[ k, n], If[ k == 1, 1, If[ n > k, T[ k, Mod[ n, k, 1]],  DivisorSigma [1, n]]]]] (* Michael Somos, Jul 18 2011 *)

PROG

(PARI) {T(n, k) = if( n<1 || k<1, 0, if( k>n, T(k, n), if( k==1, 1, if( n>k, T(k, (n-1)%k+1), sigma( n)))))} /* Michael Somos, Jul 18 2011 */

(Haskell)

a132442 n k = a132442_tabl !! (n-1) !! (k-1)

a132442_row n = a132442_tabl !! (n-1)

a132442_tabl = map (map a000203) a050873_tabl

-- Reinhard Zumkeller, Dec 12 2015

CROSSREFS

Cf. A051731, A127093, A038040 (row sums), A000203 (right border).

Cf. A050873.

Sequence in context: A284373 A104610 A138684 * A074927 A139605 A191780

Adjacent sequences:  A132439 A132440 A132441 * A132443 A132444 A132445

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 14 2007

EXTENSIONS

Missing T(10,9) = 1 inserted by Reinhard Zumkeller, Dec 12 2015

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 7 22:01 EDT 2022. Contains 355995 sequences. (Running on oeis4.)