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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 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.)