A278051 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k+k'), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n).

2, 3, 10, 35, 252, 2772, 6435, 858, 680680, 12932920, 5290740, 121687020, 1029659400, 3088978200, 582272390700, 18050444111700, 128701918800, 25740383760, 70301729698200, 10043104242600, 109530094869795600, 523310453266801200, 51193413906534900, 481218090721428060

Offset

1,1

Links

Table of n, a(n) for n=1..24.

J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187. See Eq. (20).

Example

The fractions b(n) are 1/2, 2/3, 9/10, 38/35, 347/252, 4189/2772, 11767/6435, 1733/858, 1548081/680680, 31464371/12932920, 14680543/5290740, 353517989/121687020, 3350216417/1029659400, 10571768267/3088978200, ...

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 30 do
t1:=denom(Farey(n));
t2:=add( 1/(t1[i]+t1[i+1]), i=1..nops(t1)-1);
ans:=[op(ans), t2];
od:
ans;
map(numer, ans); # A278050
map(denom, ans); # A278051

Crossrefs

Cf. A006843, A005728, A240877, A278046, A278050.

Sequence in context: A134959 A270367 A056607 * A060604 A075890 A296269

Adjacent sequences: A278048 A278049 A278050 * A278052 A278053 A278054

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 23 2016

Status

approved