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

Author

Chris Boyd, Jan 06 2019

Keywords

• nonn
• frac

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.

Examples

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

Links

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

Crossrefs

Cf. A323184.

Programs

Mathematica

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

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)", "))