A278046 Let v = list of denominators of Farey series of order n (see A006843); a(n) = sum of products of adjacent terms of v.

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

Offset: 1

Author

N. J. A. Sloane, Nov 22 2016

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A006843, A005728, A240877.

Programs

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;