The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A228812 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A228812

Triangle read by rows: T(n,k), n>=1, k>=1, in which row n lists m terms, where m = A055086(n). If k divides n and k < n^(1/2) then T(n,k) = k and T(n,m-k+1) = n/T(n,k). Also, if k^2 = n then T(n,k) = k. Other terms are zeros.
(history; published version)

#32 by Jon E. Schoenfield at Sat Mar 14 00:23:35 EDT 2015

STATUS

editing

approved

#31 by Jon E. Schoenfield at Sat Mar 14 00:23:34 EDT 2015

EXAMPLE

For n = 60 the 60-th 60th row of triangle is [1, 2, 3, 4, 5, 6, 0, 0, 10, 12, 15, 20, 30, 60]. The row length is A055086(60) = 14. The number of zeros is A078152(60) = 2. The number of positive terms is A000005(60) = 12. The positive terms are the divisors of 60. The row sum is A000203(60) = 168.

STATUS

approved

editing

#30 by Ralf Stephan at Wed Oct 30 05:33:13 EDT 2013

STATUS

proposed

approved

#29 by Omar E. Pol at Mon Oct 28 13:27:05 EDT 2013

STATUS

editing

proposed

#28 by Omar E. Pol at Mon Oct 28 13:26:28 EDT 2013

NAME

Triangle read by rows: T(n,k), n>=1, k>=1, in which row n lists m terms, where m is = A055086(n). If k divides n and k < n^(1/2) then T(n,k) = k and T(n,m-k+1) = n/T(n,k). Also, if k^2 = n then T(n,k) = k. Other terms are zeros.

STATUS

proposed

editing

#27 by Omar E. Pol at Sun Oct 27 17:39:36 EDT 2013

STATUS

editing

proposed

#26 by Omar E. Pol at Sun Oct 27 17:39:30 EDT 2013

NAME

Triangle read by rows : T(n,k), n>=1, k>=1, in which row n lists m terms, where m is A055086(n). If k divides n and k < n^(1/2) then T(n,k) = k and T(n,m-k+1) = n/T(n,k). Also, if k^2 = n then T(n,k) = k. Other terms are zeros.

STATUS

proposed

editing

#25 by Omar E. Pol at Sun Oct 27 17:30:14 EDT 2013

STATUS

editing

proposed

#24 by Omar E. Pol at Sun Oct 27 17:28:44 EDT 2013

NAME

Triangle read by rows in which row n lists m terms, where m is A055086(n). If k divides n and k < n^(1/2) then T(n,k), = k and T(n>=,m-k+1, ) = n/T(n,k). Also, if k>^2 =1, related to the divisors of n then T(see Comments lines for definitionn,k) = k. Other terms are zeros.

COMMENTS

In order to construct this sequence we use the following rules:The number of positive terms of row n is A000005(n).

- The positive terms of row n are the divisors of n in increasing order.

- The number of zeros in row n equals A078152(n).

- Row n has length A055086(n).

- If k divides n and k <= sqrt(n) then T(n,k) = k.

- The divisors q of n that are greater than sqrt(n) are located in the equidistant columns to the divisors p of n that are lesser than sqrt(n) such that n = p*q.

The number of zeros in row n equals A078152(n).

The number of positive terms of row n is A000005(n).

Discussion

Sun Oct 27

17:29

Omar E. Pol: Now there is a new definition.

#23 by Omar E. Pol at Wed Oct 23 10:50:17 EDT 2013

EXAMPLE

For n = 60 the 60-th row of triangle is [1, 2, 3, 4, 5, 6, 0, 0, 10, 12, 15, 20, 30, 60]. The row length is A055086(60) = 14. The number of zeros is A078152(60) = 2. The number of positive terms is A000005(60) = 12. The positive terms are the divisors of 60. The row sum is A000203(60) = 168.

STATUS

proposed

editing