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A371166
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Positive integers with fewer divisors (A000005) than distinct divisors of prime indices (A370820).
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6
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7, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 73, 74, 79, 89, 91, 95, 97, 101, 103, 106, 107, 111, 113, 122, 131, 137, 139, 141, 142, 143, 145, 149, 151, 159, 161, 163, 167, 169, 173, 178, 181, 183, 185, 193, 197, 199, 203, 209, 213, 214, 215, 219, 221, 223, 226
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OFFSET
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1,1
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COMMENTS
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A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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FORMULA
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EXAMPLE
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The terms together with their prime indices begin:
7: {4} 101: {26} 163: {38} 223: {48}
13: {6} 103: {27} 167: {39} 226: {1,30}
19: {8} 106: {1,16} 169: {6,6} 227: {49}
23: {9} 107: {28} 173: {40} 229: {50}
29: {10} 111: {2,12} 178: {1,24} 233: {51}
37: {12} 113: {30} 181: {42} 239: {52}
43: {14} 122: {1,18} 183: {2,18} 247: {6,8}
47: {15} 131: {32} 185: {3,12} 251: {54}
53: {16} 137: {33} 193: {44} 257: {55}
61: {18} 139: {34} 197: {45} 259: {4,12}
71: {20} 141: {2,15} 199: {46} 262: {1,32}
73: {21} 142: {1,20} 203: {4,10} 263: {56}
74: {1,12} 143: {5,6} 209: {5,8} 265: {3,16}
79: {22} 145: {3,10} 213: {2,20} 267: {2,24}
89: {24} 149: {35} 214: {1,28} 269: {57}
91: {4,6} 151: {36} 215: {3,14} 271: {58}
95: {3,8} 159: {2,16} 219: {2,21} 281: {60}
97: {25} 161: {4,9} 221: {6,7} 293: {62}
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MATHEMATICA
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Select[Range[100], Length[Divisors[#]] < Length[Union@@Divisors/@PrimePi/@First/@FactorInteger[#]]&]
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CROSSREFS
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For (equal to) instead of (less than) we have A371165, counted by A371172.
For (greater than) instead of (less than) we have A371167.
A001221 counts distinct prime factors.
A355731 counts choices of a divisor of each prime index, firsts A355732.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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