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A278048 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k*k'*(k+k')), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n).

%I A278048 #13 Nov 23 2016 02:49:31
%S A278048 2,3,30,21,252,396,6435,858,2042040,3527160,5290740,9360540,
%T A278048 1029659400,617795640,116454478140,1061790830100,283144221360,
%U A278048 10644519600,14060345939640,14060345939640,2960272834318800,130015019445168,4653946718775900,43747099156493460
%N A278048 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k*k'*(k+k')), where (k,k') are pairs of successive terms of v; a(n) = denominator of b(n).
%H A278048 J. Lehner and M. Newman, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa15/aa15114.pdf">Sums involving Farey fractions</a>, Acta Arithmetica 15.2 (1969): 181-187.
%e A278048 The fractions b(n) are 1/2, 1/3, 7/30, 4/21, 37/252, 53/396, 707/6435, 85/858, 179077/2042040, 289613/3527160, 379721/5290740, 641671/9360540, 62836087/1029659400, 35819033/617795640, ...
%p A278048 Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end:
%p A278048 ans:=[];
%p A278048 for n from 1 to 50 do
%p A278048 t1:=denom(Farey(n));
%p A278048 t2:=add( 1/(t1[i]*t1[i+1]*(t1[i]+t1[i+1])),i=1..nops(t1)-1);
%p A278048 ans:=[op(ans),t2];
%p A278048 od:
%p A278048 ans;
%p A278048 map(numer,ans); # A278047
%p A278048 map(denom,ans); # A278048
%Y A278048 Cf. A006843, A005728, A240877, A278046, A278047.
%K A278048 nonn,frac
%O A278048 1,1
%A A278048 _N. J. A. Sloane_, Nov 22 2016