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Search: id:A120249
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| A120249 |
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Numerator of cfenc[n] (see definition in comments). |
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+0
3
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| 1, 2, 3, 3, 5, 5, 8, 4, 4, 8, 13, 7, 21, 13, 7, 5, 34, 7, 55, 11, 11, 21, 89, 9, 7, 34, 5, 18, 144, 12, 233, 6, 18, 55, 12, 10, 377, 89, 29, 14, 610, 19, 987, 29, 9, 144, 1597, 11, 11, 11, 47, 47, 2584, 9, 19, 23, 76, 233, 4181, 17, 6765, 377, 14, 7, 31, 31, 10946, 76, 123, 19
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a[n] := numerator of cfenc[n]. cfenc[n] := number given by interpreting as a continued fraction expansion (indexed from 1) the sequence whose i-th entry is one plus the exponent on the i-th prime factor of n (fix cfenc[1]=1). a[2^k] = cfenc[2^k] = k+1. a[A000040[n]] = A000045[n+2].
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FORMULA
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a[1] = 1 a[n] = (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > 0, pp = First[fl]; fl = Drop[fl, 1]; pq[[PrimePi[pp[[1]]]]] = pp[[2]] + 1;]; numerator[FromContinuedFraction[pq]])
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EXAMPLE
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a[2646] = numerator[cfenc[2646]]= numerator[cfenc[2^1 * 3^3 * 7^2]] = numerator[FromContinuedFraction[{2; 4, 1, 3}]] = numerator[2 + 1/(4 + 1/(1 + 1/3))] = numerator[42/19] = 42
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MATHEMATICA
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Table[If[n == 1, 1, (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > 0, pp = First[fl]; fl = Drop[fl, 1]; pq[[PrimePi[pp[[1]]]]] = pp[[2]] + 1; ]; Numerator[FromContinuedFraction[pq]])], {n, 1, 80}]
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CROSSREFS
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Corresponding denominators in A120250. Numerators modulo respective denominators in A120251.
Adjacent sequences: A120246 A120247 A120248 this_sequence A120250 A120251 A120252
Sequence in context: A113637 A130006 A099609 this_sequence A058690 A087153 A134408
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KEYWORD
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frac,hard,nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006, Jun 25 2006
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