cp's OEIS Frontend

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

%I A323185 #18 Mar 17 2023 12:56:35
%S A323185 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,
%T A323185 33,37,29,37,31,70,34,35,36,56,37,39,40,65,41,51,43,57,53,47,47,99,50,
%U A323185 57,52,67,53,76,56,89,58,59,59,90,61,63,73,169,66,79,67,87
%N A323185 Denominators of rationals whose continued fraction representations show the prime factors of n (for n > 1) in nondecreasing order.
%C A323185 a(n) is the denominator of the generating rational of n (see comments and numerators in A323184).
%C A323185 If n is prime, a(n) is n.
%H A323185 Georg Fischer, <a href="/A323185/b323185.txt">Table of n, a(n) for n = 2..1000</a>
%e A323185 a(28) = 37 because 15/37 = [0; 2, 2, 7] and 2*2*7 = 28.
%e A323185 a(29) = 29 because 1/29 = [0; 29] = 29.
%t A323185 Array[Denominator@ FromContinuedFraction@ Prepend[Flatten@ Map[ConstantArray[ #1, #2] &  @@ # &, FactorInteger@ #], 0] &, 67, 2] (* _Michael De Vlieger_, Jan 07 2019 *)
%o A323185 (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])));}
%o A323185 A323185(n)={vectorise_factors(n); contfracpnqn(v)[2,1];}
%o A323185 for(k=2,75,print1(A323185(k)", "))
%Y A323185 Cf. A323184.
%K A323185 nonn,frac
%O A323185 2,1
%A A323185 _Chris Boyd_, Jan 06 2019