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A340690
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Numbers with a factorization whose greatest factor is 2^k, where k is the number of factors.
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4
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2, 8, 12, 16, 32, 48, 64, 72, 80, 96, 112, 120, 128, 144, 160, 168, 192, 200, 224, 240, 256, 280, 288, 320, 336, 384, 392, 432, 448, 480, 512, 576, 640, 672, 704, 720, 768, 800, 832, 864, 896, 960, 1008, 1024, 1056, 1120, 1152, 1200, 1248, 1280, 1296, 1344
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OFFSET
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1,1
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LINKS
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EXAMPLE
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The initial terms and a valid factorization of each:
2 = 2 168 = 3*7*8 512 = 2*2*2*2*32
8 = 2*4 192 = 2*2*3*16 576 = 2*2*9*16
12 = 3*4 200 = 5*5*8 640 = 2*2*10*16
16 = 4*4 224 = 4*7*8 672 = 2*3*7*16
32 = 2*2*8 240 = 5*6*8 704 = 2*2*11*16
48 = 2*3*8 256 = 2*2*4*16 720 = 3*3*5*16
64 = 2*4*8 280 = 5*7*8 768 = 2*2*2*3*32
72 = 3*3*8 288 = 2*3*3*16 800 = 2*5*5*16
80 = 2*5*8 320 = 2*2*5*16 832 = 2*2*13*16
96 = 2*6*8 336 = 6*7*8 864 = 2*3*9*16
112 = 2*7*8 384 = 2*2*6*16 896 = 2*2*14*16
120 = 3*5*8 392 = 7*7*8 960 = 2*2*15*16
128 = 2*2*2*16 432 = 3*3*3*16 1008 = 3*3*7*16
144 = 3*6*8 448 = 2*2*7*16 1024 = 2*2*2*4*32
160 = 4*5*8 480 = 2*3*5*16 1056 = 2*3*11*16
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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[1000], Select[facs[#], 2^Length[#]==Max@@#&]!={}&]
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CROSSREFS
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Partitions of the prescribed type are counted by A340611.
A047993 counts balanced partitions.
A316439 counts factorizations by product and length.
A340596 counts co-balanced factorizations.
A340597 lists numbers with an alt-balanced factorization.
A340653 counts balanced factorizations.
Cf. A106529, A117409, A200750, A325134, A340386, A340387, A340599, A340607, A340654, A340655, A340656, A340657.
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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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