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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056538 Irregular triangle read by rows: row n lists divisors of n in decreasing order. 15
1, 2, 1, 3, 1, 4, 2, 1, 5, 1, 6, 3, 2, 1, 7, 1, 8, 4, 2, 1, 9, 3, 1, 10, 5, 2, 1, 11, 1, 12, 6, 4, 3, 2, 1, 13, 1, 14, 7, 2, 1, 15, 5, 3, 1, 16, 8, 4, 2, 1, 17, 1, 18, 9, 6, 3, 2, 1, 19, 1, 20, 10, 5, 4, 2, 1, 21, 7, 3, 1, 22, 11, 2, 1, 23, 1, 24, 12, 8, 6, 4, 3, 2, 1, 25, 5, 1, 26, 13, 2, 1, 27, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Old name was "Replace n by its divisors in reverse order."

This gives the second elements of the ordered pairs (a,b), a >= 1, b >= 1, ordered by their product ab.

T(n,k) = n / A027750(n,k) = A027750(n,n-k+1), 1 <= k <= A000005(n). - Reinhard Zumkeller, Sep 28 2014

LINKS

Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened

Omar E. Pol, Illustration of the divisors of n - Omar E. Pol, Nov 22 2009

FORMULA

a(n) = A064894(A064896(n)).

EXAMPLE

Triangle begins:

1;

2, 1;

3, 1;

4, 2, 1;

5, 1;

6, 3, 2, 1;

7, 1;

8, 4, 2, 1;

9, 3, 1;

10, 5, 2, 1;

11, 1;

12, 6, 4, 3, 2, 1;

13, 1;

14, 7, 2, 1;

15, 5, 3, 1;

16, 8, 4, 2, 1;

17, 1;

18, 9, 6, 3, 2, 1;

19, 1;

20, 10, 5, 4, 2, 1;

MAPLE

map(op, [seq(reverse(sort(divisors(j))), j=1..30)]);

cdr := proc(l) if 0 = nops(l) then ([]) else (l[2..nops(l)]): fi: end:

reverse := proc(l) if 0 = nops(l) then ([]) else [op(reverse(cdr(l))), l[1]]; fi: end:

MATHEMATICA

Table[Reverse@ Divisors@ n, {n, 27}] // Flatten (* Michael De Vlieger, Jul 27 2016 *)

PROG

(MAGMA) [Reverse(Divisors(n)) : n in [1..30]];

(Haskell)

a056538 n k = a056538_tabf !! (n-1) !! (k-1)

a056538_row n = a056538_tabf !! (n-1)

a056538_tabf = map reverse a027750_tabf

-- Reinhard Zumkeller, Sep 28 2014

(PARI) row(n)=Vecrev(divisors(n)) \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Cf. A027750 for the first elements, A056534, A168017, A000005 (row lengths), A000203 (row sums).

Sequence in context: A113398 A210959 A233772 * A266742 A120385 A216477

Adjacent sequences:  A056535 A056536 A056537 * A056539 A056540 A056541

KEYWORD

nonn,tabf

AUTHOR

Antti Karttunen, Jun 20, 2000

EXTENSIONS

Definition revised by N. J. A. Sloane, Jul 27 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 21 22:56 EST 2018. Contains 299427 sequences. (Running on oeis4.)