A344368 Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(1-s)).

1, 2, 3, 8, 5, 12, 7, 24, 18, 20, 11, 48, 13, 28, 30, 80, 17, 72, 19, 80, 42, 44, 23, 168, 50, 52, 81, 112, 29, 150, 31, 224, 66, 68, 70, 324, 37, 76, 78, 280, 41, 210, 43, 176, 180, 92, 47, 576, 98, 200, 102, 208, 53, 378, 110, 392, 114, 116, 59, 660

Offset: 1

Author

Ilya Gutkovskiy, May 16 2021

Keywords

• nonn

Crossrefs

Cf. A001055, A006906, A050367, A050369, A224892, A344369, A344370.

Programs

Mathematica

T[, 1] = T[1, ] = 1; T[n_, m_] := T[n, m] = DivisorSum[n, Boole[1 < # <= m] T[n/#, #] &]; A001055[n_] := T[n, n]; Table[n A001055[n], {n, 60}]

Formula

a(n) = n * A001055(n).

a(1) = 1; a(n) = -Sum_{d|n, d < n} A224892(n/d) * a(d).