A278050 - OEIS

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A278050

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) = numerator of b(n).

1, 2, 9, 38, 347, 4189, 11767, 1733, 1548081, 31464371, 14680543, 353517989, 3350216417, 10571768267, 2114915577977, 69039991480573, 538250871701, 110983833313, 328448743696081, 48484885139543, 553270527392631611, 2736415713954900433, 286367762285513933, 2754025786313797907

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OFFSET

1,2

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