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!)
A235671 Triangle read by rows in which row n lists the proper divisors of n in increasing order, 2n, and the proper divisors of n in decreasing order. 1
2, 1, 4, 1, 1, 6, 1, 1, 2, 8, 2, 1, 1, 10, 1, 1, 2, 3, 12, 3, 2, 1, 1, 14, 1, 1, 2, 4, 16, 4, 2, 1, 1, 3, 18, 3, 1, 1, 2, 5, 20, 5, 2, 1, 1, 22, 1, 1, 2, 3, 4, 6, 24, 6, 4, 3, 2, 1, 1, 26, 1, 1, 2, 7, 28, 7, 2, 1, 1, 3, 5, 30, 5, 3, 1, 1, 2, 4, 8, 32, 8, 4, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numerators of a sequence related to the symmetric structure of sigma, which arises from the structure of A237593. The structure in the first two octants is transformed in a structure in the 6th and 7th octants, which is similar to an isosceles triangle.

Denominators are in A007395.

Row sums give A074400.

Row lengths is A114003 (see the Jovovic's formula in A114003).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

The irregular triangle begins:

2;

1, 4, 1;

1, 6, 1;

1, 2, 8, 2, 1;

1, 10, 1;

1, 2, 3, 12, 3, 2, 1;

1, 14, 1;

1, 2, 4, 16, 4, 2, 1;

1, 3, 18, 3, 1;

1, 2, 5, 20, 5, 2, 1;

1, 22, 1;

1, 2, 3, 4, 6, 24, 6, 4, 3, 2, 1;

...

Also:

1;

1/2, 2, 1/2;

1/2, 3, 1/2;

1/2, 1, 4, 1, 1/2;

1/2, 5, 1/2;

1/2, 1, 3/2, 6, 3/2, 1, 1/2;

1/2, 7, 1/2;

1/2, 1, 2, 8, 2, 1, 1/2;

1/2, 3/2, 9, 3/2, 1/2;

1/2, 1, 5/2, 10, 5/2, 1, 1/2;

1/2, 11, 1/2;

1/2, 1, 3/2, 2, 3, 12, 3, 2, 3/2, 1, 1/2;

...

MATHEMATICA

pd[n_]:=Module[{d=Most[Divisors[n]]}, Flatten[Join[{d, {2n}, Reverse[d]}]]]; Flatten[Array[pd, 20]] (* Harvey P. Dale, Dec 22 2014 *)

CROSSREFS

Cf. A000005, A001065, A027750, A056538, A074400, A000203, A114002, A114003, A236104, A237591, A237593, A237270, A233772, A233773.

Sequence in context: A062866 A131035 A118745 * A131034 A130313 A247073

Adjacent sequences:  A235668 A235669 A235670 * A235672 A235673 A235674

KEYWORD

nonn,frac,tabf

AUTHOR

Omar E. Pol, Jan 24 2014

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 February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)