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EXAMPLE
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The sequence of terms together with their prime indices begins:
8: {1,1,1} 105: {2,3,4}
16: {1,1,1,1} 108: {1,1,2,2,2}
24: {1,1,1,2} 110: {1,3,5}
27: {2,2,2} 112: {1,1,1,1,4}
30: {1,2,3} 120: {1,1,1,2,3}
32: {1,1,1,1,1} 125: {3,3,3}
40: {1,1,1,3} 128: {1,1,1,1,1,1,1}
48: {1,1,1,1,2} 135: {2,2,2,3}
54: {1,2,2,2} 136: {1,1,1,7}
56: {1,1,1,4} 144: {1,1,1,1,2,2}
60: {1,1,2,3} 150: {1,2,3,3}
64: {1,1,1,1,1,1} 152: {1,1,1,8}
72: {1,1,1,2,2} 160: {1,1,1,1,1,3}
80: {1,1,1,1,3} 162: {1,2,2,2,2}
81: {2,2,2,2} 168: {1,1,1,2,4}
88: {1,1,1,5} 176: {1,1,1,1,5}
96: {1,1,1,1,1,2} 184: {1,1,1,9}
104: {1,1,1,6} 189: {2,2,2,4}
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