A240877 Sum of the denominators of the Farey series of order n (A006843).

1, 2, 4, 10, 18, 38, 50, 92, 124, 178, 218, 328, 376, 532, 616, 736, 864, 1136, 1244, 1586, 1746, 1998, 2218, 2724, 2916, 3416, 3728, 4214, 4550, 5362, 5602, 6532, 7044, 7704, 8248, 9088, 9520, 10852, 11536, 12472, 13112, 14752, 15256, 17062, 17942, 19022, 20034, 22196, 22964, 25022, 26022

Offset: 0

Author

Robert G. Wilson v, Apr 13 2014

Keywords

• nonn

Comments

All terms except a(0) are even.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000010, A006842, A006843, A011755, A185197, A213544.

Programs

Mathematica

Farey[n_] := Union[ Flatten[ Join[{0}, Table[a/b, {b, n}, {a, b}]]]]; Table[ Total[ Denominator[ Farey[ n]]], {n, 0, 50}]

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

Formula

a(n) = 1 + Sum_{k=1..n} k*A000010(k). - Isaac Saffold, Dec 03 2017

a(n) = 1 + A011755(n). - Michel Marcus, Dec 23 2017

a(n) ~ c * n^3, where c = 2/Pi^2 (A185197). - Amiram Eldar, Dec 01 2023