A049688 a(n) = Sum_{i=0..n} T(i,n-i), array T as in A049687.

0, 2, 5, 10, 17, 28, 41, 60, 83, 112, 145, 188, 235, 294, 359, 432, 513, 610, 713, 834, 963, 1104, 1255, 1428, 1609, 1810, 2023, 2254, 2497, 2768, 3047, 3356, 3681, 4026, 4387, 4772, 5169, 5602, 6053, 6528, 7019

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Comments

A131967(a(n)+1) = 1, A131967(a(n)) = 2. - Birkas Gyorgy, Feb 19 2011

Number of triples {A, B, C} where 1 <= A <= B <= C <= n+1 and gcd(C-B, B-A) = 1. E.g., for n=2, we have the 5 triples {1, 1, 2}, {1, 2, 2}, {2, 2, 3}, {2, 3, 3}, and {1, 2, 3}. - Griffin N. Macris, May 21 2016

Links

• Griffin N. Macris, Table of n, a(n) for n = 0..99999

Crossrefs

Cf. A049687, A131967.

Programs

Mathematica

Table[Sum[Sum[EulerPhi[j], {j, i}] + 1, {i, n}], {n, 0, 30}] (* Birkas Gyorgy, Feb 19 2011 *)
Table[n + Sum[ EulerPhi[ j], {i, n}, {j, i}], {n, 0, 30}] (* Robert G. Wilson v, Feb 12 2015 *)

Formula

a(n) ~ n^2*(3+n) / Pi^2. - Griffin N. Macris, May 21 2016