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A278046 Let v = list of denominators of Farey series of order n (see A006843); a(n) = sum of products of adjacent terms of v. 6
1, 4, 18, 44, 124, 186, 424, 636, 1038, 1378, 2368, 2852, 4516, 5510, 7030, 8734, 12542, 14168, 19526, 22206, 26658, 30728, 40342, 44190, 54590, 61402, 72328, 80196, 99684, 105644, 129514, 143162, 161422, 176926, 201566, 214538, 255386, 277160, 307736, 329096, 384856, 402412, 466826, 499166 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Note that the sum of the reciprocals of these products is 1.

LINKS

Table of n, a(n) for n=1..44.

J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187.

EXAMPLE

When n = 4, v = [1,4,3,2,3,4,1], so a(4) = 1*4 + 4*3 + 3*2 + 2*3 + 3*4 + 4*1 = 44.

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( t1[i]*t1[i+1], i=1..nops(t1)-1);

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

od:

ans;

CROSSREFS

Cf. A006843, A005728, A240877.

Sequence in context: A126283 A023618 A115077 * A258634 A280599 A066153

Adjacent sequences:  A278043 A278044 A278045 * A278047 A278048 A278049

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 22 2016

STATUS

approved

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Last modified June 23 17:39 EDT 2021. Contains 345402 sequences. (Running on oeis4.)