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A330977
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Numbers whose number of factorizations into factors > 1 (A001055) is a power of 2.
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13
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1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 82, 83, 85, 86, 87
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OFFSET
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1,2
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COMMENTS
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The complement starts: 8, 16, 24, 27, 30, 32, 36, 40.
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LINKS
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EXAMPLE
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Factorizations of n = 1, 4, 12, 72:
() (4) (12) (72)
(2*2) (2*6) (8*9)
(3*4) (2*36)
(2*2*3) (3*24)
(4*18)
(6*12)
(2*4*9)
(2*6*6)
(3*3*8)
(3*4*6)
(2*2*18)
(2*3*12)
(2*2*2*9)
(2*2*3*6)
(2*3*3*4)
(2*2*2*3*3)
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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]]}]];
Select[Range[100], IntegerQ[Log[2, Length[facs[#]]]]&]
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CROSSREFS
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The same for strict integer partitions is A331022.
The least number with exactly n factorizations is A330973(n).
The least number with exactly 2^n factorizations is A330989(n).
Numbers whose inverse prime shadow belongs to this sequence are A330990.
Numbers with a prime number of factorizations are A330991.
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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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