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A278047 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) = numerator of b(n). 2
1, 1, 7, 4, 37, 53, 707, 85, 179077, 289613, 379721, 641671, 62836087, 35819033, 6367281023, 55181728027, 13442946373, 490167893, 596530310479, 576997238399, 116144361532321, 4931206160615, 164890340129357, 1514840590670747, 10181612956306486603, 3295813969039399097 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..26.

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

Cf. A006843, A005728, A240877, A278046, A278048.

Sequence in context: A270732 A270468 A270983 * A271007 A271053 A270629

Adjacent sequences:  A278044 A278045 A278046 * A278048 A278049 A278050

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Nov 22 2016

STATUS

approved

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Last modified September 22 13:47 EDT 2020. Contains 337289 sequences. (Running on oeis4.)