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EXAMPLE
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The sequence of terms together with their prime indices begins:
4: {1,1} 80: {1,1,1,1,3}
8: {1,1,1} 81: {2,2,2,2}
9: {2,2} 88: {1,1,1,5}
16: {1,1,1,1} 96: {1,1,1,1,1,2}
24: {1,1,1,2} 104: {1,1,1,6}
25: {3,3} 108: {1,1,2,2,2}
27: {2,2,2} 112: {1,1,1,1,4}
32: {1,1,1,1,1} 121: {5,5}
40: {1,1,1,3} 125: {3,3,3}
48: {1,1,1,1,2} 128: {1,1,1,1,1,1,1}
49: {4,4} 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}
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}
For example, a complete list of strict factorizations of 72 is: (2*3*12), (2*4*9), (2*36), (3*4*6), (3*24), (4*18), (6*12), (8*9), (72); but since none of these consists of only primes or squarefree semiprimes, 72 is in the sequence.
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