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A111796
Positive integers sorted by rote weight (A062537) and omega (A001221).
1
1, 2, 3, 4, 5, 7, 8, 9, 16, 6, 11, 13, 17, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536, 10, 12, 14, 18
OFFSET
1,2
COMMENTS
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).
EXAMPLE
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
KEYWORD
nonn,tabf
AUTHOR
Jon Awbrey, Sep 01 2005
STATUS
approved