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

Author

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

Keywords

• frac
• nonn
• uned

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).

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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}]

Formula

a(2^k) = 1.

a(prime(n)) = Fibonacci(n+1).