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%I #24 Dec 01 2023 04:44:00
%S 1,2,4,10,18,38,50,92,124,178,218,328,376,532,616,736,864,1136,1244,
%T 1586,1746,1998,2218,2724,2916,3416,3728,4214,4550,5362,5602,6532,
%U 7044,7704,8248,9088,9520,10852,11536,12472,13112,14752,15256,17062,17942,19022,20034,22196,22964,25022,26022
%N Sum of the denominators of the Farey series of order n (A006843).
%C All terms except a(0) are even.
%H Charles R Greathouse IV, <a href="/A240877/b240877.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = 1 + Sum_{k=1..n} k*A000010(k). - _Isaac Saffold_, Dec 03 2017
%F a(n) = 1 + A011755(n). - _Michel Marcus_, Dec 23 2017
%F a(n) ~ c * n^3, where c = 2/Pi^2 (A185197). - _Amiram Eldar_, Dec 01 2023
%t Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[ Total[ Denominator[ Farey[ n]]], {n, 0, 50}]
%o (PARI) first(n)=my(s=1,v=vector(n+1)); v[1]=1; forfactored(k=1,n, v[k[1]+1]=s+=k[1]*eulerphi(k)); v \\ _Charles R Greathouse IV_, Dec 27 2017
%Y Cf. A000010, A006842, A006843, A011755, A185197, A213544.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Apr 13 2014
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