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A111796 Positive integers sorted by rote weight (A062537) and omega (A001221).

%I A111796 #6 Nov 23 2013 23:44:50
%S A111796 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,
%T A111796 65536,10,12,14,18
%N A111796 Positive integers sorted by rote weight (A062537) and omega (A001221).
%C A111796 Positive integers m sorted by g(m) = A062537(m) and w(m) = A001221(m).
%C A111796 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).
%H A111796 J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>
%e A111796 Table of Integers, Primal Codes, Sort Parameters and Subtotals
%e A111796 ` ` a ` code` ` | g w | s | t
%e A111796 ----------------+-----+---+---
%e A111796 ` ` 1 = { } ` ` | 0 0 | 1 | 1
%e A111796 ----------------+-----+---+---
%e A111796 ` ` 2 = 1:1 ` ` | 1 1 | 1 | 1
%e A111796 ----------------+-----+---+---
%e A111796 ` ` 3 = 2:1 ` ` | 2 1 | ` |
%e A111796 ` ` 4 = 1:2 ` ` | 2 1 | 2 | 2
%e A111796 ----------------+-----+---+---
%e A111796 ` ` 5 = 3:1 ` ` | 3 1 | ` |
%e A111796 ` ` 7 = 4:1 ` ` | 3 1 | ` |
%e A111796 ` ` 8 = 1:3 ` ` | 3 1 | ` |
%e A111796 ` ` 9 = 2:2 ` ` | 3 1 | ` |
%e A111796 ` `16 = 1:4 ` ` | 3 1 | 5 |
%e A111796 ----------------+-----+---+---
%e A111796 ` ` 6 = 1:1 2:1 | 3 2 | 1 | 6
%e A111796 ----------------+-----+---+---
%e A111796 ` `11 = 5:1 ` ` | 4 1 | ` |
%e A111796 ` `13 = 6:1 ` ` | 4 1 | ` |
%e A111796 ` `17 = 7:1 ` ` | 4 1 | ` |
%e A111796 ` `19 = 8:1 ` ` | 4 1 | ` |
%e A111796 ` `23 = 9:1 ` ` | 4 1 | ` |
%e A111796 ` `25 = 3:2 ` ` | 4 1 | ` |
%e A111796 ` `27 = 2:3 ` ` | 4 1 | ` |
%e A111796 ` `32 = 1:5 ` ` | 4 1 | ` |
%e A111796 ` `49 = 4:2 ` ` | 4 1 | ` |
%e A111796 ` `53 = 16:1` ` | 4 1 | ` |
%e A111796 ` `64 = 1:6 ` ` | 4 1 | ` |
%e A111796 ` `81 = 2:4 ` ` | 4 1 | ` |
%e A111796 ` 128 = 1:7 ` ` | 4 1 | ` |
%e A111796 ` 256 = 1:8 ` ` | 4 1 | ` |
%e A111796 ` 512 = 1:9 ` ` | 4 1 | ` |
%e A111796 65536 = 1:16` ` | 4 1 |16 |
%e A111796 ----------------+-----+---+---
%e A111796 ` `10 = 1:1 3:1 | 4 2 | ` |
%e A111796 ` `12 = 1:2 2:1 | 4 2 | ` |
%e A111796 ` `14 = 1:1 4:1 | 4 2 | ` |
%e A111796 ` `18 = 1:1 2:2 | 4 2 | 4 |20
%e A111796 ----------------+-----+---+---
%e A111796 a = this sequence
%e A111796 g = rote weight in gammas = A062537
%e A111796 w = rote wayage in gammas = A001221
%e A111796 s = count in (g, w) class = A111797
%e A111796 t = count in weight class = A061396
%Y A111796 Cf. A001221, A061396, A062504, A062537, A062860.
%Y A111796 Cf. A111797, A111798, A111800.
%K A111796 nonn,tabf
%O A111796 1,2
%A A111796 _Jon Awbrey_, Sep 01 2005