The On-Line Encyclopedia of Integer Sequences (OEIS)

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A299693

Irregular triangle read by rows in which row n lists the total sum of the divisors of all numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n); or row n is 0 if no such k exists.
(history; published version)

#22 by N. J. A. Sloane at Sun Jun 24 11:23:03 EDT 2018

STATUS

editing

approved

#21 by N. J. A. Sloane at Sun Jun 24 11:22:42 EDT 2018

NAME

Irregular triangle read by rows in which row n lists the total sum of the divisor divisors of all numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n), ; or row n is 0 if no such k exists.

FORMULA

T(n,m) = A000203(A279385(n,m), if A279385(n,m) > 0, otherwise T(n,m) = 0.

STATUS

proposed

editing

Discussion

Sun Jun 24

11:22

N. J. A. Sloane: grammatical edits

#20 by Omar E. Pol at Wed Jun 20 09:55:46 EDT 2018

STATUS

editing

proposed

#19 by Omar E. Pol at Wed Jun 20 09:55:17 EDT 2018

COMMENTS

a(j) is also the total area of the terraces at the A279385(j)-th level, starting from the top, of the stepped pyramid described in A245092.

FORMULA

aT(jn,m) = A000203(A279385(jn,m), if A279385(jn,m) is positive, > 0, otherwise aT(jn,m) = 0, with j >= 1.

#18 by Omar E. Pol at Wed Jun 20 09:05:02 EDT 2018

EXAMPLE

-------------------------------------------

j A000203 Diagram

-------------------------------------------

. _ _ _ _ _ _ _ _ _ _ _ _

1 1 |_| | | | | | | | | | | |

2 3 |_ _|_| | | | | | | | | |

3 4 |_ _| _|_| | | | | | | |

4 7 |_ _ _| _|_| | | | | |

5 6 |_ _ _| _| _ _|_| | | |

6 12 |_ _ _ _| _| | _ _|_| |

7 8 |_ _ _ _| |_ _|_| _ _|

8 15 |_ _ _ _ _| _| |

9 13 |_ _ _ _ _| | _|

10 18 |_ _ _ _ _ _| _ _|

11 12 |_ _ _ _ _ _| |

12 28 |_ _ _ _ _ _ _|

.

#17 by Omar E. Pol at Wed Jun 20 09:01:24 EDT 2018

DATA

1, 3, 4, 7, 6, 0, 12, 8, 15, 13, 18, 12, 0, 28, 14, 24, 0, 24, 31, 18, 39, 20, 0, 42, 32, 36, 24, 0, 60, 31, 42, 40, 0, 56, 30, 0, 72, 32, 63, 48, 54, 0, 48, 91, 38, 60, 56, 0, 90, 42, 0, 96, 44, 84, 0, 78, 72, 48, 0, 124, 57, 93, 72, 98, 54, 0, 120, 72, 0, 120, 80, 90, 60, 0, 168, 62, 96, 0, 104, 127, 84, 0

KEYWORD

nonn,tabl,more,tabf,changed

#16 by Omar E. Pol at Wed Jun 20 08:58:32 EDT 2018

DATA

1, 3, 4, 7, 6, 0, 12, 8, 15, 13, 18, 12, 0, 28, 14, 24, 0, 24, 31, 18, 39, 20, 0, 42, 32, 36, 24, 0

EXAMPLE

0;

#15 by Omar E. Pol at Sun Jun 10 17:42:59 EDT 2018

CROSSREFS

Cf. A071562, A196020, A235791, A236104, A237048, A237591, A237593, A240542, A244050, A245092, A276112, A277437, A279286, A279385, A280912, A280919, A280223, A282131, A282197, A280295, A281012.

Discussion

Sun Jun 17

23:13

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A299693 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#14 by Omar E. Pol at Sun Jun 10 17:41:33 EDT 2018

CROSSREFS

Cf. A071562, A196020, A235791, A236104, A237048, A237591, A237593, A240542, A244050, A245092, A276112, A277437, A279286, A279385, A280912, A280919, A280223, A282131, A282197, A280295, A281012.

#13 by Omar E. Pol at Sun Jun 10 13:33:14 EDT 2018

NAME

Irregular triangle read by rows Irregular triangle read by rows in which row n lists the total sum of the divisor of all numbers k such that the largest Dyck path of the symmetric representation of sigma(k) contains the point (n,n), or row n is 0 if no such k exists.