A307967 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

1, 1, 1, 1, 3, 3, 6, 5, 11, 8, 14, 16, 20, 16, 37, 22, 34, 49, 44, 36, 90, 46, 73, 108, 80, 75, 181, 89, 121, 210, 151, 123, 334, 153, 197, 368, 227, 219, 567, 229, 313, 613, 365, 315, 871, 367, 461, 986, 519, 463, 1355, 534, 660, 1429, 756, 662, 1960, 794, 940, 2054

Offset: 1

Author

Ilya Gutkovskiy, May 11 2019

Keywords

• nonn

Comments

Shifts 3 places left when inverse Moebius transform applied twice.

Crossrefs

Cf. A000005, A007557, A307982, A307993, A308083, A319133.

Programs

Mathematica

a[n_] := a[n] = Sum[DivisorSigma[0, (n - 3)/d] a[d], {d, Divisors[n - 3]}]; a[1] = a[2] = a[3] = 1; Table[a[n], {n, 1, 60}]

Formula

a(1) = a(2) = a(3) = 1; a(n+3) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).