OFFSET
1,13
COMMENTS
Conjecture: a(n) >= 1 for n >= 15.
FORMULA
Conjecture: a(n) << n/log(n) (see links for the graph of a(n)/n*log(n)).
Does the limit of a(n)*log(n)/n as n tends to infinity exist?
MATHEMATICA
c[x_] := Length @ ContinuedFraction[x] ; a[n_] := Count[Range[n], _?(c[(n/#)^2] == 2 * c[n/#] &)]; Array[a, 100] (* Amiram Eldar, Oct 04 2020 *)
PROG
(PARI) L(n, q)=length(contfrac(n/q));
a(n)=sum(k=1, n, if(L(n, k)*2-L(n^2, k^2), 0, 1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Oct 04 2020
STATUS
approved