A278561 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) = denominator of b(n).

2, 3, 10, 7, 252, 396, 6435, 858, 680680, 1175720, 5290740, 9360540, 1029659400, 617795640, 116454478140, 1061790830100, 283144221360, 74511637200, 14060345939640, 14060345939640, 109530094869795600, 650075097225840, 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. (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, A278052 (numerators).

Sequence in context: A333176 A338043 A141670 * A369991 A193729 A303115

Adjacent sequences: A278558 A278559 A278560 * A278562 A278563 A278564

Keyword

nonn,frac

Author

N. J. A. Sloane, Nov 23 2016

Status

approved