OFFSET
1,2
COMMENTS
Note that the sum of the reciprocals of these products is 1.
LINKS
J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187.
EXAMPLE
When n = 4, v = [1,4,3,2,3,4,1], so a(4) = 1*4 + 4*3 + 3*2 + 2*3 + 3*4 + 4*1 = 44.
MAPLE
Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end:
ans:=[];
for n from 1 to 50 do
t1:=denom(Farey(n));
t2:=add( t1[i]*t1[i+1], i=1..nops(t1)-1);
ans:=[op(ans), t2];
od:
ans;
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 22 2016
STATUS
approved