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A331201
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Numbers k such that the number of factorizations of k into distinct factors > 1 is a prime number.
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5
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6, 8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 80, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 102
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OFFSET
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1,1
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COMMENTS
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First differs from A080257 in lacking 60.
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LINKS
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EXAMPLE
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Strict factorizations of selected terms:
(6) (12) (24) (48) (216)
(2*3) (2*6) (3*8) (6*8) (3*72)
(3*4) (4*6) (2*24) (4*54)
(2*12) (3*16) (6*36)
(2*3*4) (4*12) (8*27)
(2*3*8) (9*24)
(2*4*6) (12*18)
(2*108)
(3*8*9)
(4*6*9)
(2*3*36)
(2*4*27)
(2*6*18)
(2*9*12)
(3*4*18)
(3*6*12)
(2*3*4*9)
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MATHEMATICA
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strfacs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[strfacs[n/d], Min@@#>d&]], {d, Rest[Divisors[n]]}]];
Select[Range[100], PrimeQ[Length[strfacs[#]]]&]
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CROSSREFS
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The version for strict integer partitions is A035359.
The version for integer partitions is A046063.
The version for set partitions is A051130.
Numbers whose number of strict factorizations is odd are A331230.
Numbers whose number of strict factorizations is even are A331231.
The least number with n strict factorizations is A330974(n).
Cf. A001318, A045780, A318286, A328966, A330992, A330993, A330997, A331023/A331024, A331050, A331051, A331200, A331232.
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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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