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A371168
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Positive integers with fewer prime factors (A001222) than distinct divisors of prime indices (A370820).
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14
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3, 5, 7, 11, 13, 14, 15, 17, 19, 21, 23, 26, 29, 31, 33, 35, 37, 38, 39, 41, 43, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 65, 67, 69, 70, 71, 73, 74, 76, 77, 78, 79, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 105, 106, 107, 109, 111, 113, 114, 115
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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 prime indices of 105 are {2,3,4}, and there are 3 prime factors (3,5,7) and 4 distinct divisors of prime indices (1,2,3,4), so 105 is in the sequence.
The terms together with their prime indices begin:
3: {2} 35: {3,4} 59: {17} 86: {1,14}
5: {3} 37: {12} 61: {18} 87: {2,10}
7: {4} 38: {1,8} 65: {3,6} 89: {24}
11: {5} 39: {2,6} 67: {19} 91: {4,6}
13: {6} 41: {13} 69: {2,9} 93: {2,11}
14: {1,4} 43: {14} 70: {1,3,4} 94: {1,15}
15: {2,3} 46: {1,9} 71: {20} 95: {3,8}
17: {7} 47: {15} 73: {21} 97: {25}
19: {8} 49: {4,4} 74: {1,12} 101: {26}
21: {2,4} 51: {2,7} 76: {1,1,8} 103: {27}
23: {9} 52: {1,1,6} 77: {4,5} 105: {2,3,4}
26: {1,6} 53: {16} 78: {1,2,6} 106: {1,16}
29: {10} 55: {3,5} 79: {22} 107: {28}
31: {11} 57: {2,8} 83: {23} 109: {29}
33: {2,5} 58: {1,10} 85: {3,7} 111: {2,12}
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MATHEMATICA
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Select[Range[100], PrimeOmega[#]<Length[Union @@ Divisors/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]]&]
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CROSSREFS
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For divisors instead of prime factors on the LHS we get A371166.
The complement is counted by A371169.
Partitions of this type are counted by A371173.
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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