1,2

Positive integers m sorted by g(m) = A062537(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).

Table of Integers, Primal Codes, Sort Parameters and Subtotals

` ` a ` code` ` | g w | s | t

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

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

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

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

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

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

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

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

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

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

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

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

` `16 = 1:4 ` ` | 3 1 | 5 |

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

` ` 6 = 1:1 2:1 | 3 2 | 1 | 6

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

` `11 = 5:1 ` ` | 4 1 | ` |

` `13 = 6:1 ` ` | 4 1 | ` |

` `17 = 7:1 ` ` | 4 1 | ` |

` `19 = 8:1 ` ` | 4 1 | ` |

` `23 = 9:1 ` ` | 4 1 | ` |

` `25 = 3:2 ` ` | 4 1 | ` |

` `27 = 2:3 ` ` | 4 1 | ` |

` `32 = 1:5 ` ` | 4 1 | ` |

` `49 = 4:2 ` ` | 4 1 | ` |

` `53 = 16:1` ` | 4 1 | ` |

` `64 = 1:6 ` ` | 4 1 | ` |

` `81 = 2:4 ` ` | 4 1 | ` |

` 128 = 1:7 ` ` | 4 1 | ` |

` 256 = 1:8 ` ` | 4 1 | ` |

` 512 = 1:9 ` ` | 4 1 | ` |

65536 = 1:16` ` | 4 1 |16 |

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

` `10 = 1:1 3:1 | 4 2 | ` |

` `12 = 1:2 2:1 | 4 2 | ` |

` `14 = 1:1 4:1 | 4 2 | ` |

` `18 = 1:1 2:2 | 4 2 | 4 |20

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

a = this sequence

g = rote weight in gammas = A062537

w = rote wayage in gammas = A001221

s = count in (g, w) class = A111797

t = count in weight class = A061396

Cf. A001221, A061396, A062504, A062537, A062860.

Cf. A111797, A111798, A111800.

Sequence in context: A102363 A155900 A107684 this_sequence A039124 A056759 A101511

Adjacent sequences: A111793 A111794 A111795 this_sequence A111797 A111798 A111799

nonn,tabf

Jon Awbrey (jawbrey(AT)att.net), Sep 01 2005