OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..1433
Sebastian Zuniga Alterman, Explicit averages of square-free supported functions: to the edge of the convolution method, Colloquium Mathematicum, Vol. 168 (2022), pp. 1-23; arXiv preprint, arXiv:2003.05887 [math.NT], 2020.
Olivier Ramaré, Explicit average orders: news and problems, Banach Center Publications, Vol. 118 (2019), pp. 153-176.
FORMULA
a(n)/A354418(n) ~ (6/Pi^2) * (log(n) + c) + O*(1.044/sqrt(n)), where f = O*(g) means |f| <= g and c = gamma + 2 * Sum_{p prime} log(p)/(p^2-1) = A001620 + 2 * A306016 = 1.71713765109059847340... (Ramaré, 2019; Alterman, 2022). - Amiram Eldar, Oct 29 2022
EXAMPLE
1, 3/2, 11/6, 61/30, 11/5, 82/35, 171/70, 1951/770, 26133/10010, 13424/5005, 41273/15015, ...
MAPLE
s:= 0: R:= NULL: count:= 0:
for x from 1 while count < 40 do
if numtheory:-issqrfree(x) then
s:= s + 1/x;
v:= numer(s);
R:= R, v;
count:= count+1;
fi;
od:
R; # Robert Israel, Mar 05 2023
MATHEMATICA
Accumulate[1/Select[Range[43], SquareFreeQ]] // Numerator
PROG
(PARI) a(n) = my(i=0, s=0); for(x=1, oo, if(core(x)==x, s+=1/x; i++; if(i==n, return(numerator(s))))) \\ Felix Fröhlich, May 26 2022
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Ilya Gutkovskiy, May 26 2022
STATUS
approved