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A359911
Number of integer factorizations of n into factors > 1 without the same mean as median.
6
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 0, 1, 0, 1, 1, 0, 0, 6, 0, 1, 0, 1, 0, 3, 0, 3, 0, 0, 0, 4, 0, 0, 1, 4, 0, 1, 0, 1, 0, 1, 0, 9, 0, 0, 1, 1, 0, 1, 0, 6, 1, 0, 0, 5, 0, 0, 0
OFFSET
1,24
EXAMPLE
The a(72) = 9 factorizations: (2*2*2*3*3), (2*2*2*9), (2*2*3*6), (2*2*18), (2*3*12), (2*4*9), (2*6*6), (3*3*8), (3*4*6).
MATHEMATICA
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}]
CROSSREFS
The version for partitions is A359894, complement A240219.
The complement is counted by A359909, odd-length A359910.
A001055 counts factorizations.
A326622 counts factorizations with integer mean, strict A328966.
Sequence in context: A277735 A248911 A116681 * A131371 A319195 A003475
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 24 2023
STATUS
approved