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A360248
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Numbers for which the prime indices do not have the same median as the distinct prime indices.
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23
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12, 18, 20, 24, 28, 40, 44, 45, 48, 50, 52, 54, 56, 60, 63, 68, 72, 75, 76, 80, 84, 88, 92, 96, 98, 99, 104, 108, 112, 116, 117, 120, 124, 132, 135, 136, 140, 144, 147, 148, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 184, 188, 189, 192, 200
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OFFSET
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1,1
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COMMENTS
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First differs from A242416 in lacking 180, with prime indices {1,1,2,2,3}.
First differs from A360246 in lacking 126 and having 1950.
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.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
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LINKS
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EXAMPLE
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The terms together with their prime indices begin:
12: {1,1,2}
18: {1,2,2}
20: {1,1,3}
24: {1,1,1,2}
28: {1,1,4}
40: {1,1,1,3}
44: {1,1,5}
45: {2,2,3}
48: {1,1,1,1,2}
50: {1,3,3}
52: {1,1,6}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
63: {2,2,4}
68: {1,1,7}
72: {1,1,1,2,2}
The prime indices of 126 are {1,2,2,4} with median 2 and distinct prime indices {1,2,4} with median 2, so 126 is not in the sequence.
The prime indices of 1950 are {1,2,3,3,6} with median 3 and distinct prime indices {1,2,3,6} with median 5/2, so 1950 is in the sequence.
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MATHEMATICA
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prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Median[prix[#]]!=Median[Union[prix[#]]]&]
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CROSSREFS
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These partitions are counted by A360244.
For multiplicities instead of parts: complement of A360453.
For multiplicities instead of distinct parts: complement of A360454.
The complement for mean instead of median is A360247, counted by A360243.
A360005 gives median of prime indices (times two).
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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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