A341639 a(1) = 1; a(n+1) = Sum_{d|n} phi(d) * a(d) * a(n/d).

1, 1, 2, 6, 19, 95, 291, 2037, 10203, 71429, 357240, 3929640, 19648533, 255430929, 1788018540, 16092167088, 144829514049, 2462101738833, 17234712244012, 327459532636228, 2947135794083881, 38312765323095109, 421440418557975839, 9693129626833444297, 87238166641520673597

Offset: 1

Author

Ilya Gutkovskiy, Feb 16 2021

Keywords

• nonn

Crossrefs

Cf. A000010, A038044, A038045, A332791.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[EulerPhi[d] a[d] a[(n - 1)/d], {d, Divisors[n - 1]}]; Table[a[n], {n, 25}]
a[1] = 1; a[n_] := a[n] = Sum[a[GCD[n - 1, k]] a[(n - 1)/GCD[n - 1, k]], {k, n - 1}]; Table[a[n], {n, 25}]

Formula

a(1) = 1; a(n+1) = Sum_{k=1..n} a(gcd(n,k)) * a(n/gcd(n,k)).