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!)
A212119 Triangle read by rows T(n,k), n>=1, k>=1, where T(n,k) is the number of divisors d of n with min(d, n/d) = k. 13
1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column k lists the numbers A040000: 1, 2, 2, 2, 2... interleaved with k-1 zeros, starting in row k^2.

The sum of row n gives A000005(n), the number of divisors of n.

T(n,k) is also the number of divisors of n on the edges of k-th triangle in the diagram of divisors (see link section). See also A212120.

It appears that there are only eight rows that do not contain zeros. The indices of these rows are 1, 2, 3, 4, 6, 8, 12, 24, the divisors of 24, see A018253. - Omar E. Pol, Dec 03 2013

LINKS

Table of n, a(n) for n=1..85.

Omar E. Pol, Diagram of divisors, figure 1, figure 2

Omar E. Pol, Illustration of initial terms and of row sums

EXAMPLE

Row 10 gives 2, 2, 0 therefore the sums of row 10 is 2+2+0 = 4, the same as A000005(10), the number of divisors of 10.

Written as an irregular triangle the sequence begins:

1;

2;

2;

2, 1;

2, 0;

2, 2;

2, 0;

2, 2;

2, 0, 1;

2, 2, 0;

2, 0, 0;

2, 2, 2;

2, 0, 0;

2, 2, 0;

2, 0, 2;

2, 2, 0, 1;

2, 0, 0, 0;

2, 2, 2, 0;

2, 0, 0, 0;

2, 2, 0, 2;

2, 0, 2, 0;

2, 2, 0, 0;

2, 0, 0, 0;

2, 2, 2, 2;

2, 0, 0, 0, 1;

CROSSREFS

Row sums give A000005. Column 1 is A040000. Column 2 gives the absolute values of A176742.

Cf. A006218, A027750, A010766, A147861, A163100, A196020, A210959, A212120, A211343, A221645, A228812-A228814.

Sequence in context: A210673 A129320 A320844 * A096831 A191516 A168141

Adjacent sequences:  A212116 A212117 A212118 * A212120 A212121 A212122

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Jul 02 2012

EXTENSIONS

Definition changed by Franklin T. Adams-Watters, Jul 12 2012

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 January 27 08:31 EST 2020. Contains 331293 sequences. (Running on oeis4.)