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A059529
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For 1 < x, each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(0),...,c(n-1) so that 1 c(0) x^1 c(1) x^2,.., c(n-1) x^n is an integer.
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10
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1, 1, 2, 5, 9, 16, 32, 68, 135, 256, 512, 1059, 2110, 4096, 8192, 16745, 33425, 65536, 131072, 266254, 531924, 1048576, 2097152, 4244214, 8482454, 16777216, 33554432, 67741466, 135417620, 268435456, 536870912, 1082015434, 2163280087, 4294967296, 8589934592
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OFFSET
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0,3
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COMMENTS
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From Gus Wiseman, Jul 04 2019: (Start)
Also the number of subsets of {1..n} whose sum is less than or equal to the sum of their complement. For example, the a(0) = 1 through a(5) = 16 subsets are:
{} {} {} {} {} {}
{1} {1} {1} {1}
{2} {2} {2}
{3} {3} {3}
{1,2} {4} {4}
{1,2} {5}
{1,3} {1,2}
{1,4} {1,3}
{2,3} {1,4}
{1,5}
{2,3}
{2,4}
{2,5}
{3,4}
{1,2,3}
{1,2,4}
(End)
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LINKS
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Table of n, a(n) for n=0..34.
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FORMULA
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a(0)=1; for 0<n, a(n) = A058377(n)+2^(n-1).
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EXAMPLE
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x = 3: for n = 2 there are 2 possibilities: 1*3*9=27 and 1/3*9=3. For n = 4 there are 9 possibilities: 1*3*9*27*81 1/3*9*27*81 1*3/9*27*81 1/3/9*27*81 1*3*9/27*81 1*3*9*27/81 1/3*9/27*81 1/3*9*27/81 1*3/9/27*81
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], Plus@@Complement[Range[n], #]>=Plus@@#&]], {n, 0, 10}] (* Gus Wiseman, Jul 04 2019 *)
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CROSSREFS
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Cf. A058524, A058377.
Cf. A053632, A063865, A326173, A326174, A326175.
Sequence in context: A039946 A130752 A309331 * A271318 A119676 A348836
Adjacent sequences: A059526 A059527 A059528 * A059530 A059531 A059532
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KEYWORD
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nonn
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AUTHOR
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Naohiro Nomoto, Feb 16 2001
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EXTENSIONS
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More terms from Alois P. Heinz, Jun 13 2019
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STATUS
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approved
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