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A359910
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Number of odd-length integer factorizations of n into factors > 1 with the same mean as median.
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14
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0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,8
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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 = 120, 960, 5760, 6720:
120 960 5760 6720
4*5*6 2*16*30 16*18*20 4*30*56
2*6*10 4*12*20 3*5*6*8*8 10*21*32
8*10*12 4*4*6*6*10 12*20*28
3*4*4*4*5 2*2*8*10*18 4*5*6*7*8
2*2*2*4*4*5*9 2*4*7*10*12
2*2*2*4*5*6*7
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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], OddQ[Length[#]]&&Mean[#]==Median[#]&]], {n, 100}]
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CROSSREFS
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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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