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A360460
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Two times the median of the unordered prime signature of n; a(1) = 1.
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16
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1, 2, 2, 4, 2, 2, 2, 6, 4, 2, 2, 3, 2, 2, 2, 8, 2, 3, 2, 3, 2, 2, 2, 4, 4, 2, 6, 3, 2, 2, 2, 10, 2, 2, 2, 4, 2, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 5, 4, 3, 2, 3, 2, 4, 2, 4, 2, 2, 2, 2, 2, 2, 3, 12, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 5, 8, 2, 2, 2, 2, 2, 2
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OFFSET
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1,2
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COMMENTS
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The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). Since the denominator is always 1 or 2, the median can be represented as an integer by multiplying by 2.
A number's unordered prime signature (row n of A118914) is the multiset of positive exponents in its prime factorization.
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LINKS
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EXAMPLE
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The unordered prime signature of 2520 is {1,1,2,3}, with median 3/2, so a(2520) = 3.
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MATHEMATICA
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Table[If[n==1, 1, 2*Median[Last/@FactorInteger[n]]], {n, 100}]
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CROSSREFS
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The version for divisors is A063655.
The version for prime indices is A360005.
The version for distinct prime indices is A360457.
The version for distinct prime factors is A360458.
The version for prime factors is A360459.
Positions of even terms are A360553.
Positions of odd terms are A360554.
The version for 0-prepended differences is A360555.
A304038 lists distinct prime indices.
A329976 counts partitions with median multiplicity 1.
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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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