A278561 -id:A278561 - cp's OEIS frontend

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

N. J. A. Sloane, Nov 23 2016

			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, ...

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

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

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

cp's OEIS Frontend

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).

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