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A359909
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Number of integer factorizations of n into factors > 1 with the same mean as median.
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9
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0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 5, 2, 2, 3, 3, 1, 4, 1, 4, 2, 2, 2, 6, 1, 2, 2, 4, 1, 4, 1, 3, 3, 2, 1, 6, 2, 3, 2, 3, 1, 4, 2, 4, 2, 2, 1, 7, 1, 2, 3, 7, 2, 4, 1, 3, 2, 4, 1, 7, 1, 2, 3, 3, 2, 4, 1, 6, 4, 2, 1, 6, 2, 2, 2
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OFFSET
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1,4
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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).
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LINKS
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EXAMPLE
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The a(n) factorizations for n = 24, 36, 60, 120, 144, 360:
24 36 60 120 144 360
3*8 4*9 2*30 2*60 2*72 4*90
4*6 6*6 3*20 3*40 3*48 5*72
2*12 2*18 4*15 4*30 4*36 6*60
2*3*4 3*12 5*12 5*24 6*24 8*45
2*2*3*3 6*10 6*20 8*18 9*40
3*4*5 8*15 9*16 10*36
10*12 12*12 12*30
4*5*6 2*2*6*6 15*24
2*6*10 3*3*4*4 18*20
2*3*4*5 2*180
3*120
2*10*18
3*4*5*6
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MATHEMATICA
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facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Table[Length[Select[facs[n], Mean[#]==Median[#]&]], {n, 100}]
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CROSSREFS
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These multisets are ranked by A359889.
The version for strict partitions is A359897.
The complement is counted by A359911.
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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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