OFFSET
1,3
COMMENTS
Since Sum_{k|n} k * Sum_{1<=m<=k, gcd(m,k)=1} 1/m = n*H(n), Sum_{k>=1} (Sum_{1<=m<=k, gcd(m,k)=1} 1/m) /k^2 = 2. - Leroy Quet, Nov 13 2004
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..450
FORMULA
Sum_{1<=m<=n, gcd(m,n)=1} 1/m = (1/n)*Sum_{k|n} mu(n/k)*k*H(k), where H(k) = Sum_{j=1..k} 1/j. - Leroy Quet, Nov 13 2004
EXAMPLE
a(8) = 1*3*5*7*(1 + 1/3 + 1/5 + 1/7) = 176 because 1, 3, 5 and 7 are the positive integers <= 8 that are relatively prime to 8.
MAPLE
a:= n-> (l-> mul(i, i=l)*add(1/i, i=l))(
select(x-> igcd(x, n)=1, [$1..n])):
seq(a(n), n=1..40); # Alois P. Heinz, May 22 2015
MATHEMATICA
f[n_] := Block[{k = Select[Range[n], GCD[ #, n] == 1 &]}, Plus @@ (Times @@ k*Plus @@ 1/k)]; Table[ f[n], {n, 25}] (* Robert G. Wilson v, Nov 16 2004 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Leroy Quet, Aug 30 2000
STATUS
approved