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A111798 Positive integers sorted by rote height (A109301) and omega (A001221). 3
1, 2, 3, 4, 9, 6, 12, 18, 36, 5, 7, 8, 13, 16, 23, 25, 27, 37, 49, 61, 64, 81, 125, 151, 169, 343, 512, 529, 625, 729, 1369, 2197, 2401, 3721, 4096, 12167, 15625, 19683, 22801, 28561, 50653, 117649, 226981, 262144, 279841, 531441, 1874161, 1953125, 3442951 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Positive integers m sorted by h(m) = A109301(m) and w(m) = A001221(m).

Defining the "wayage" of a rooted tree to be its root degree, the rote corresponding to the positive integer m has a wayage of w(m) = omega(m) = A001221(m).

LINKS

Table of n, a(n) for n=1..49.

J. Awbrey, Riffs and Rotes

EXAMPLE

Table of Primal Functions, Codes, Sort Parameters and Subtotals

Primal Function | ` ` ` ` ` Primal Code ` ` = ` ` a | h w | s | t

----------------+-----------------------------------+-----+---+---

{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 | 1 | 1

----------------+-----------------------------------+-----+---+---

1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 | 1 | 1

----------------+-----------------------------------+-----+---+---

2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 1 | ` |

1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 1 | ` |

2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 9 | 2 1 | 3 |

----------------+-----------------------------------+-----+---+---

1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 6 | 2 2 | ` |

1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `12 | 2 2 | ` |

1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `18 | 2 2 | ` |

1:2 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `36 | 2 2 | 4 | 7

----------------+-----------------------------------+-----+---+---

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 1 | ` |

1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `16 | 3 1 | ` |

1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `64 | 3 1 | ` |

1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 512 | 3 1 | ` |

1:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `4096 | 3 1 | ` |

1:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `262144 | 3 1 | ` |

1:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 68719476736 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `27 | 3 1 | ` |

2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `81 | 3 1 | ` |

2:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 729 | 3 1 | ` |

2:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 19683 | 3 1 | ` |

2:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `531441 | 3 1 | ` |

2:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 387420489 | 3 1 | ` |

2:36` ` ` ` ` ` | ` ` ` ` ` ` ` `150094635296999121 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 1 | ` |

4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 1 | ` |

6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `13 | 3 1 | ` |

9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `23 | 3 1 | ` |

12:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `37 | 3 1 | ` |

18:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `61 | 3 1 | ` |

36:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 151 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `25 | 3 1 | ` |

4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `49 | 3 1 | ` |

6:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 169 | 3 1 | ` |

9:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 529 | 3 1 | ` |

12:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `1369 | 3 1 | ` |

18:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `3721 | 3 1 | ` |

36:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 22801 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

3:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 125 | 3 1 | ` |

3:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 625 | 3 1 | ` |

3:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 15625 | 3 1 | ` |

3:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 1953125 | 3 1 | ` |

3:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 244140625 | 3 1 | ` |

3:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 3814697265625 | 3 1 | ` |

3:36` ` ` ` ` ` | ` ` ` `14551915228366851806640625 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

4:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 343 | 3 1 | ` |

4:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `2401 | 3 1 | ` |

4:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `117649 | 3 1 | ` |

4:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `40353607 | 3 1 | ` |

4:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 13841287201 | 3 1 | ` |

4:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` `1628413597910449 | 3 1 | ` |

4:36` ` ` ` ` ` | ` 2651730845859653471779023381601 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

6:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `2197 | 3 1 | ` |

6:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 28561 | 3 1 | ` |

6:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 4826809 | 3 1 | ` |

6:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 10604499373 | 3 1 | ` |

6:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `23298085122481 | 3 1 | ` |

6:18` ` ` ` ` ` | ` ` ` ` ` ` 112455406951957393129 | 3 1 | ` |

6:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 13^36 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

9:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 12167 | 3 1 | ` |

9:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `279841 | 3 1 | ` |

9:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 148035889 | 3 1 | ` |

9:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 1801152661463 | 3 1 | ` |

9:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` 21914624432020321 | 3 1 | ` |

9:18` ` ` ` ` ` | ` ` ` ` 3244150909895248285300369 | 3 1 | ` |

9:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 23^36 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

12:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 50653 | 3 1 | ` |

12:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 1874161 | 3 1 | ` |

12:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `2565726409 | 3 1 | ` |

12:9` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` 129961739795077 | 3 1 | ` |

12:12 ` ` ` ` ` | ` ` ` ` ` ` ` 6582952005840035281 | 3 1 | ` |

12:18 ` ` ` ` ` | ` ` 16890053810563300749953435929 | 3 1 | ` |

12:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 37^36 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

18:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `226981 | 3 1 | ` |

18:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `13845841 | 3 1 | ` |

18:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 51520374361 | 3 1 | ` |

18:9` ` ` ` ` ` | ` ` ` ` ` ` ` ` 11694146092834141 | 3 1 | ` |

18:12 ` ` ` ` ` | ` ` ` ` ` `2654348974297586158321 | 3 1 | ` |

18:18 ` ` ` ` ` | 136753052840548005895349735207881 | 3 1 | ` |

18:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 61^36 | 3 1 | ` |

` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |

36:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 3442951 | 3 1 | ` |

36:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 519885601 | 3 1 | ` |

36:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `11853911588401 | 3 1 | ` |

36:9` ` ` ` ` ` | ` ` ` ` ` ` `40812436757196811351 | 3 1 | ` |

36:12 ` ` ` ` ` | ` ` ` 140515219945627518837736801 | 3 1 | ` |

36:18 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `151^18 | 3 1 | ` |

36:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `151^36 | 3 1 |77 |

----------------+-----------------------------------+-----+---+---

The last part is left unsorted to show the method of construction.

a (when sorted ) = this sequence

h = rote height in gammas = A109301

w = rote wayage in gammas = A001221

s = count in (h, w) class = A111799

t = count in height class = A109300

CROSSREFS

Cf. A000079, A001221, A007097, A014221, A050924.

Cf. A061396, A062504, A062537, A062860, A106177.

Cf. A109300, A109301, A111791 to A111800, A112095, A112096.

Sequence in context: A277711 A060866 A064478 * A249543 A307404 A307405

Adjacent sequences:  A111795 A111796 A111797 * A111799 A111800 A111801

KEYWORD

nonn,tabf

AUTHOR

Jon Awbrey, Sep 01 2005 - Sep 10 2005

STATUS

approved

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Last modified July 23 14:24 EDT 2019. Contains 325254 sequences. (Running on oeis4.)