A307982 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

1, 1, 1, 1, 1, 3, 3, 6, 3, 11, 5, 15, 8, 19, 7, 36, 10, 31, 15, 60, 12, 56, 17, 97, 24, 72, 19, 170, 29, 94, 32, 229, 31, 156, 34, 334, 47, 182, 46, 471, 49, 218, 68, 658, 51, 314, 70, 797, 84, 354, 72, 1173, 93, 437, 98, 1353, 95, 576, 114, 1792, 131, 640, 116, 2243, 133

Offset

1,6

Comments

Shifts 4 places left when inverse Moebius transform applied twice.

Links

Table of n, a(n) for n=1..65.

Formula

a(1) = ... = a(4) = 1; a(n+4) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

Mathematica

a[n_] := a[n] = Sum[DivisorSigma[0, (n - 4)/d] a[d], {d, Divisors[n - 4]}]; a[1] = a[2] = a[3] = a[4] = 1; Table[a[n], {n, 1, 65}]

Crossrefs

Cf. A000005, A007557, A307967, A307994, A308083, A319133.

Sequence in context: A184389 A163163 A323349 * A339335 A120909 A086222

Adjacent sequences: A307979 A307980 A307981 * A307983 A307984 A307985

Keyword

nonn

Author

Ilya Gutkovskiy, May 11 2019

Status

approved