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A120250
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Denominator of cfenc(n) (see definition in comments).
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3
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1, 1, 2, 1, 3, 2, 5, 1, 3, 3, 8, 2, 13, 5, 5, 1, 21, 3, 34, 3, 8, 8, 55, 2, 4, 13, 4, 5, 89, 5, 144, 1, 13, 21, 7, 3, 233, 34, 21, 3, 377, 8, 610, 8, 7, 55, 987, 2, 7, 4, 34, 13, 1597, 4, 11, 5, 55, 89, 2584, 5, 4181, 144, 11, 1, 18, 13, 6765, 21, 89, 7, 10946, 3, 17711, 233, 7, 34
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OFFSET
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1,3
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COMMENTS
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a(n) := denominator 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) = 1; a(prime(n)) = Fibonacci(n+1).
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LINKS
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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] > Denominator[FromContinuedFraction[pq]])
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EXAMPLE
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a(2646) = denominator(cfenc(2646)) = denominator(cfenc(2^1 * 3^3 * 7^2)) = denominator(FromContinuedFraction[{2; 4, 1, 3}]) = denominator(2 + 1/(4 + 1/(1 + 1/3))) = denominator(42/19) = 19.
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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; ]; Denominator[FromContinuedFraction[pq]])], {n, 1, 80}]
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CROSSREFS
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Corresponding numerators in A120249. Numerators modulo respective denominators in A120251.
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KEYWORD
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frac,nonn,uned
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006
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STATUS
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approved
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