A278052 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum k*k'/(k+k'), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).

1, 4, 39, 52, 4069, 8573, 258017, 46639, 53371999, 113518551, 768140741, 1560819091, 242830653007, 169134016817, 38186305937387, 408881289764107, 143220706672837, 41293923006131, 9928250098118791, 10936700271572951, 97615258031147892517, 643700119549549507, 62211198375587838727

Offset

1,2

Links

Table of n, a(n) for n=1..23.

J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187. See Eq. (21).

Example

The fractions b(n) are 1/2, 4/3, 39/10, 52/7, 4069/252, 8573/396, 258017/6435, 46639/858, 53371999/680680, 113518551/1175720, 768140741/5290740, 1560819091/9360540, 242830653007/1029659400, 169134016817/617795640, 38186305937387/116454478140, ...

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( t1[i]*t1[i+1]/(t1[i]+t1[i+1]), i=1..nops(t1)-1);
od:
ans;
map(numer, ans); # A278052
map(denom, ans); # A278561

Crossrefs

Cf. A006843, A005728, A240877, A278046-A278051, A278561 (denominators).

Sequence in context: A286877 A018860 A016484 * A093850 A297736 A286359

Adjacent sequences: A278049 A278050 A278051 * A278053 A278054 A278055

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 23 2016

Status

approved