A308083 G.f. A(x) satisfies: A(x) = x + x^2 + x^3 + x^4 + x^5 * (1 + Sum_{i>=1} Sum_{j>=1} A(x^(i*j))).

1, 1, 1, 1, 1, 1, 3, 3, 6, 3, 9, 5, 12, 11, 11, 11, 22, 14, 23, 19, 29, 24, 41, 25, 40, 41, 48, 43, 66, 45, 71, 67, 86, 68, 95, 73, 113, 110, 118, 107, 157, 115, 162, 148, 182, 159, 225, 164, 235, 229, 247, 227, 296, 244, 328, 297, 357, 298, 413, 352, 452, 409, 436, 415, 575

Offset

1,7

Comments

Shifts 5 places left when inverse Moebius transform applied twice.

Links

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

Formula

a(1) = ... = a(5) = 1; a(n+5) = Sum_{d|n} tau(n/d)*a(d), where tau = number of divisors (A000005).

Mathematica

a[n_] := a[n] = Sum[DivisorSigma[0, (n - 5)/d] a[d], {d, Divisors[n - 5]}]; a[1] = a[2] = a[3] = a[4] = a[5] = 1; Table[a[n], {n, 1, 65}]

Crossrefs

Cf. A000005, A007557, A307967, A307982, A307995, A319133.

Sequence in context: A260152 A358223 A130695 * A181788 A112163 A058587

Adjacent sequences: A308080 A308081 A308082 * A308084 A308085 A308086

Keyword

nonn

Author

Ilya Gutkovskiy, May 11 2019

Status

approved