A278048 - OEIS

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).

2, 3, 30, 21, 252, 396, 6435, 858, 2042040, 3527160, 5290740, 9360540, 1029659400, 617795640, 116454478140, 1061790830100, 283144221360, 10644519600, 14060345939640, 14060345939640, 2960272834318800, 130015019445168, 4653946718775900, 43747099156493460

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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.

EXAMPLE

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, ...

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 50 do

t1:=denom(Farey(n));

t2:=add( 1/(t1[i]*t1[i+1]*(t1[i]+t1[i+1])), i=1..nops(t1)-1);

ans:=[op(ans), t2];

od:

ans;

map(numer, ans); # A278047

map(denom, ans); # A278048

CROSSREFS