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A371179
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Positive integers with fewer distinct prime factors (A001221) than distinct divisors of prime indices (A370820).
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3
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3, 5, 7, 9, 11, 13, 14, 15, 17, 19, 21, 23, 25, 26, 27, 28, 29, 31, 33, 35, 37, 38, 39, 41, 43, 45, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 61, 63, 65, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 97, 98, 99, 101
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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:
3: {2} 28: {1,1,4} 52: {1,1,6} 74: {1,12}
5: {3} 29: {10} 53: {16} 75: {2,3,3}
7: {4} 31: {11} 55: {3,5} 76: {1,1,8}
9: {2,2} 33: {2,5} 56: {1,1,1,4} 77: {4,5}
11: {5} 35: {3,4} 57: {2,8} 78: {1,2,6}
13: {6} 37: {12} 58: {1,10} 79: {22}
14: {1,4} 38: {1,8} 59: {17} 81: {2,2,2,2}
15: {2,3} 39: {2,6} 61: {18} 83: {23}
17: {7} 41: {13} 63: {2,2,4} 85: {3,7}
19: {8} 43: {14} 65: {3,6} 86: {1,14}
21: {2,4} 45: {2,2,3} 67: {19} 87: {2,10}
23: {9} 46: {1,9} 69: {2,9} 89: {24}
25: {3,3} 47: {15} 70: {1,3,4} 91: {4,6}
26: {1,6} 49: {4,4} 71: {20} 92: {1,1,9}
27: {2,2,2} 51: {2,7} 73: {21} 93: {2,11}
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MATHEMATICA
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Select[Range[100], PrimeNu[#]<Length[Union @@ Divisors/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]]&]
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CROSSREFS
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Counting all prime indices on the LHS gives A371168, counted by A371173.
A008284 counts partitions by length.
A305148 counts pairwise indivisible (stable) partitions, ranks A316476.
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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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