Help with definition of sequence

[Andrew Plewe]

I'd like to submit the following sequence to the OEIS.  Usually I can 
find enough information to cobble together something that more-or-less 
makes sense to the average reader.  However, in this case I'm at a loss 
for how, exactly, to describe this sequence.  It is constructed as 
follows:


1,						1
2,	1,					3
3,	2,	1,				6
4,						4
5,	3,	2,	1,			11
6,						6
7,	4,					11
8,						8
9,						9
10,						10
11,	5,	3,	2,	1,		22
12,						12
13,	6,					19
14,						14
15,						15
16,						16
17,	7,	4,				28
18,						18
19,	8,					27
20,						20
21,						21
22,						22
23,	9,					32
24,						24
25,						25
26,						26
27,						27
28,						28
29,	10,					39
30,						30
31,	11,	5,	3,	2,	1,	53
32,						32
33,						33
34,						34
35,						35
36,						36
37,	12,					49
38,						38
39,						39
40,						40
41,	13,	6,				60
42,						42
43,	14,					57
44,						44
45,						45
46,						46
47,	15,					62
48,						48
49,						49
50,						50
51,						51
52,						52
53,	16,					69
54,						54
55,						55
56,						56
57,						57
58,						58
59,	17,	7,	4,			87



The sequence itself is in the rightmost column, i.e. 1, 3, 6, 4, 11, 6, 
11, 8, 9, 10, 22, etc., which is the sum of each line.  As you can see, 
it's essentially based on the primeth sequences (see, for example, 
A007097).  Where I'm running into trouble is in figuring out how to 
word a short description of the sequence.  Any suggestions?  Thanks!
	-Andrew Plewe-