A120250 Denominator of cfenc(n) (see definition in comments).

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

Offset

1,3

Comments

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).

Links

Hans Havermann, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; a(n) = (fl = FactorInteger[n]; pq = Table[1, {i, 1, PrimePi[Last[fl][[1]]]}]; While[Length[fl] > Denominator[FromContinuedFraction[pq]])

Example

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.

Mathematica

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}]

Crossrefs

Corresponding numerators in A120249. Numerators modulo respective denominators in A120251.

Sequence in context: A117364 A193615 A300383 * A280689 A352961 A116529

Adjacent sequences: A120247 A120248 A120249 * A120251 A120252 A120253

Keyword

frac,nonn,uned

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 12 2006

Status

approved