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EXAMPLE
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The prime factorization of 600 is 2*2*2*3*5*5, and 3 > max(1,2), so 600 is in the sequence.
The prime factorization of 180 is 2*2*3*3*5, but 2 <= max(2,1), so 180 is not in the sequence.
The terms together with their prime indices begin:
1: {} 29: {10} 67: {19}
2: {1} 31: {11} 68: {1,1,7}
3: {2} 32: {1,1,1,1,1} 71: {20}
4: {1,1} 37: {12} 72: {1,1,1,2,2}
5: {3} 40: {1,1,1,3} 73: {21}
7: {4} 41: {13} 76: {1,1,8}
8: {1,1,1} 43: {14} 79: {22}
9: {2,2} 44: {1,1,5} 80: {1,1,1,1,3}
11: {5} 45: {2,2,3} 81: {2,2,2,2}
12: {1,1,2} 47: {15} 83: {23}
13: {6} 48: {1,1,1,1,2} 84: {1,1,2,4}
16: {1,1,1,1} 49: {4,4} 88: {1,1,1,5}
17: {7} 52: {1,1,6} 89: {24}
19: {8} 53: {16} 92: {1,1,9}
20: {1,1,3} 56: {1,1,1,4} 96: {1,1,1,1,1,2}
23: {9} 59: {17} 97: {25}
24: {1,1,1,2} 60: {1,1,2,3} 99: {2,2,5}
25: {3,3} 61: {18} 101: {26}
27: {2,2,2} 63: {2,2,4} 103: {27}
28: {1,1,4} 64: {1,1,1,1,1,1} 104: {1,1,1,6}
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