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A326647
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Number of factorizations of n into factors > 1 with integer average and integer geometric mean.
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14
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0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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1,4
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LINKS
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EXAMPLE
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The a(216) = 5 factorizations:
(2*4*27)
(3*3*24)
(3*6*12)
(6*6*6)
(216)
The a(729) = 8 factorizations:
(3*3*3*3*3*3)
(3*3*81)
(3*9*27)
(3*243)
(9*9*9)
(9*81)
(27*27)
(729)
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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], IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 2, 100}]
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CROSSREFS
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Positions of terms > 1 are the perfect powers A001597.
Factorizations with integer average are A326622.
Factorizations with integer geometric mean are A326028.
Partitions with integer average and geometric mean are A326641.
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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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