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A371169
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Positive integers with at least as many prime factors (A001222) as distinct divisors of prime indices (A370820).
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7
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1, 2, 4, 6, 8, 9, 10, 12, 16, 18, 20, 22, 24, 25, 27, 28, 30, 32, 34, 36, 40, 42, 44, 45, 48, 50, 54, 56, 60, 62, 63, 64, 66, 68, 72, 75, 80, 81, 82, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 108, 110, 112, 118, 120, 121, 124, 125, 126, 128, 132, 134, 135
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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.
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LINKS
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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}
9: {2,2}
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}
25: {3,3}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
34: {1,7}
36: {1,1,2,2}
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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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The version for prime factors instead of divisors on the RHS is A319899.
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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