A323185 Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.

2, 3, 5, 5, 7, 7, 12, 10, 11, 11, 17, 13, 15, 16, 29, 17, 23, 19, 27, 22, 23, 23, 41, 26, 27, 33, 37, 29, 37, 31, 70, 34, 35, 36, 56, 37, 39, 40, 65, 41, 51, 43, 57, 53, 47, 47, 99, 50, 57, 52, 67, 53, 76, 56, 89, 58, 59, 59, 90, 61, 63, 73, 169, 66, 79, 67, 87

Offset

2,1

Comments

a(n) is the denominator of the generating rational of n (see comments and numerators in A323184).

If n is prime, a(n) is n.

Links

Georg Fischer, Table of n, a(n) for n = 2..1000

Example

a(28) = 37 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.
a(29) = 29 because 1/29 = [0; 29] = 29.

Mathematica

Array[Denominator@ FromContinuedFraction@ Prepend[Flatten@ Map[ConstantArray[ #1, #2] &  @@ # &, FactorInteger@ #], 0] &, 67, 2] (* Michael De Vlieger, Jan 07 2019 *)

Prog

(PARI) vectorise_factors(m)={v=[0]; F=factor(m); for(i=1, matsize(F)[1], for(j=1, F[i, 2], v=concat(v, F[i, 1]))); }
A323185(n)={vectorise_factors(n); contfracpnqn(v)[2, 1]; }
for(k=2, 75, print1(A323185(k)", "))

Crossrefs

Cf. A323184.

Sequence in context: A082432 A336298 A037153 * A168065 A077724 A163867

Adjacent sequences: A323182 A323183 A323184 * A323186 A323187 A323188

Keyword

nonn,frac

Author

Chris Boyd, Jan 06 2019

Status

approved