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A371177
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Positive integers whose prime indices include all distinct divisors of all prime indices.
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15
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1, 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 30, 32, 34, 36, 40, 42, 44, 48, 50, 54, 60, 62, 64, 66, 68, 72, 80, 82, 84, 88, 90, 96, 100, 102, 108, 110, 118, 120, 124, 126, 128, 132, 134, 136, 144, 150, 160, 162, 164, 166, 168, 170, 176, 180, 186, 192, 198, 200
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OFFSET
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1,2
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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.
Also positive integers with as many distinct prime factors (A001221) as distinct divisors of prime indices (A370820).
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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:
1: {}
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
22: {1,5}
24: {1,1,1,2}
30: {1,2,3}
32: {1,1,1,1,1}
34: {1,7}
36: {1,1,2,2}
40: {1,1,1,3}
42: {1,2,4}
44: {1,1,5}
48: {1,1,1,1,2}
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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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A008284 counts partitions by length.
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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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