A105861 a(n) = (n/2) * Sum_{k=0..n} binomial(n,k)/gcd(n,k).

1, 3, 10, 23, 76, 102, 442, 695, 1792, 2828, 11254, 13334, 53236, 65418, 155110, 347319, 1114096, 1259328, 4980718, 6223148, 15033700, 27548678, 96468970, 108761942, 352992576, 529504212, 1381165192, 2314603370, 7784628196

Offset: 1

Author

Robert G. Wilson v, Apr 23 2005

Keywords

• nonn

Comments

If instead the limits of the summation run from 1 to n-1, then the sum is A105861(n)-1.

Crossrefs

Cf. A105862, A105863.

Programs

Mathematica

f[n_] := n*Sum[ Binomial[n, k] / GCD[n, k], {k, 0, n}]/2; Table[ f[n], {n, 30}]

PARI

a(n) = sum(k=0, n, binomial(n, k)/gcd(n, k))*n/2; \\ Michel Marcus, Oct 19 2019

Formula

a(n) = (n/2) * Sum_{k=0..n} binomial(n, k) / gcd(n, k).