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EXAMPLE
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The sequence of rooted trees ranked by this sequence together with their Matula-Goebel numbers begins:
1: o
2: (o)
4: (oo)
6: (o(o))
8: (ooo)
9: ((o)(o))
12: (oo(o))
14: (o(oo))
16: (oooo)
18: (o(o)(o))
24: (ooo(o))
26: (o(o(o)))
27: ((o)(o)(o))
28: (oo(oo))
32: (ooooo)
36: (oo(o)(o))
38: (o(ooo))
46: (o((o)(o)))
48: (oooo(o))
49: ((oo)(oo))
The sequence of terms together with their prime indices begins:
1: {} 52: {1,1,6} 152: {1,1,1,8}
2: {1} 54: {1,2,2,2} 162: {1,2,2,2,2}
4: {1,1} 56: {1,1,1,4} 169: {6,6}
6: {1,2} 64: {1,1,1,1,1,1} 172: {1,1,14}
8: {1,1,1} 72: {1,1,1,2,2} 178: {1,24}
9: {2,2} 74: {1,12} 184: {1,1,1,9}
12: {1,1,2} 76: {1,1,8} 192: {1,1,1,1,1,1,2}
14: {1,4} 81: {2,2,2,2} 196: {1,1,4,4}
16: {1,1,1,1} 86: {1,14} 202: {1,26}
18: {1,2,2} 92: {1,1,9} 206: {1,27}
24: {1,1,1,2} 96: {1,1,1,1,1,2} 208: {1,1,1,1,6}
26: {1,6} 98: {1,4,4} 212: {1,1,16}
27: {2,2,2} 104: {1,1,1,6} 214: {1,28}
28: {1,1,4} 106: {1,16} 216: {1,1,1,2,2,2}
32: {1,1,1,1,1} 108: {1,1,2,2,2} 224: {1,1,1,1,1,4}
36: {1,1,2,2} 112: {1,1,1,1,4} 243: {2,2,2,2,2}
38: {1,8} 122: {1,18} 244: {1,1,18}
46: {1,9} 128: {1,1,1,1,1,1,1} 256: {1,1,1,1,1,1,1,1}
48: {1,1,1,1,2} 144: {1,1,1,1,2,2} 262: {1,32}
49: {4,4} 148: {1,1,12} 288: {1,1,1,1,1,2,2}
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