OFFSET
1,2
COMMENTS
Does lim_{n -> infinity} a(n)/n = 3/2?
Sum_{k=1..n} 1/gcd(n,k) = (1/n)*Sum_{d|n} phi(d)*d = (1/n)*Sum_{k=1..n} gcd(n,k)*phi(gcd(n,k))/phi(n/gcd(n,k)), where phi = A000010. - Richard L. Ollerton, May 10 2021
The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 9, 78, 709, 6713, 65135, 637603, 6275585, 61972835, 613362869, 6080312594, ... . Apparently, the asymptotic density of this sequence is 0 and the limit in the question above is infinite. - Amiram Eldar, Jun 28 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
Sum_{k=1..12} 1/gcd(12,k) = 77/12 hence 12 is in the sequence.
MATHEMATICA
Select[Range[100], Denominator[Sum[1/GCD[#, k], {k, #}]]==#&] (* Harvey P. Dale, Dec 13 2011 *)
PROG
(PARI) for(n=1, 300, if(denominator(sum(i=1, n, 1/gcd(n, i))) == n, print1(n, ", ")))
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 18 2002
STATUS
approved