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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
2, 3, 10, 7, 252, 396, 6435, 858, 680680, 1175720, 5290740, 9360540, 1029659400, 617795640, 116454478140, 1061790830100, 283144221360, 74511637200, 14060345939640, 14060345939640, 109530094869795600, 650075097225840, 51193413906534900, 481218090721428060 (list; graph; refs; listen; history; text; internal format)
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 * A193729 A303115 A074068

Adjacent sequences:  A278558 A278559 A278560 * A278562 A278563 A278564

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 23 2016

STATUS

approved

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Last modified June 22 18:49 EDT 2021. Contains 345388 sequences. (Running on oeis4.)