maybe a more compact way of looking at the prime powers in the denominator:
here \( 08002222022000022222222221 \rightarrow 2^{0} 3^{8} 5^{0} 7^{0} 11^{2} 13^{2} 17^{2} 19^{2} 23^{0} 29^{2} 31^{2} 37^{0} 41^{0} 43^{0} 47^{0} 53^{2} 59^{2} 61^{2} 67^{2} 71^{2} 73^{2} 79^{2} 83^{2} 89^{2} 97^{2} 101^{1} \)
The carats under each line indicate the prime factors of n... and a * next to n represents prime n.
Code:
n prime exponents in denominator from p=3..101]
50 08002222022000022222222221
^ ^
49 06401222022000022222222220
^
48 04440222022000022222222210
^^
*47 06340221022000022222222200
^
46 05240220021000222222222200
^ ^
45 04230120220000222222222200
^^
44 08420020220000222222222100
^ ^
*43 07422020210000222222222000
^
42 06322010200002222222222000
^^ ^
*41 08242000200002222222221000
^
40 04242000200022222222220000
^ ^
39 00442000200022222222210000
^ ^
38 02431200200022222222200000
^ ^
*37 01220202200022222222200000
^
36 00020202200222222222100000
^^
35 04020202200222222221000000
^^
34 03240202100222222220000000
^ ^
33 02240222000222222210000000
^ ^
32 04142122000222222200000000
^
*31 02032022000222222200000000
^
30 00022022002222222100000000
^^^
*29 02222022002222221000000000
^
28 01222021022222220000000000
^ ^
27 00141020022222220000000000
^
26 06040020022222210000000000
^ ^
25 05040210022222200000000000
^
24 04420200022222200000000000
^^
*23 06400200022222100000000000
^
22 04300200222222000000000000
^ ^
21 02202200222221000000000000
^ ^
20 04222200222210000000000000
^ ^
*19 03422100222200000000000000
^
18 02422002222100000000000000
^^
*17 06312002222000000000000000
^
16 05201022222000000000000000
^
15 04200022221000000000000000
^^
14 06400022210000000000000000
^ ^
*13 03420022200000000000000000
^
12 00220222200000000000000000
^^
*11 02020222100000000000000000
^
10 01012222000000000000000000
^ ^
9 00202221000000000000000000
^
8 04202210000000000000000000
^
*7 03102200000000000000000000
^
6 02022100000000000000000000
^^
*5 04021000000000000000000000
^
4 02220000000000000000000000
^
*3 00210000000000000000000000
^
*2 02100000000000000000000000
^
1 01000000000000000000000000