sage: L = LazyDirichletSeriesRing(ZZ, "z")
sage: g = L(constant=1); g
1 + 1/(2^z) + 1/(3^z) + ...
sage: g*g
1 + 2/2^z + 2/3^z + 3/4^z + 2/5^z + 4/6^z + 2/7^z + ...
sage: [number_of_divisors(n) for n in range(1, 8)]
[1, 2, 2, 3, 2, 4, 2]

sage: mu = L(moebius); mu
1 + -1/2^z + -1/3^z + -1/5^z + 1/(6^z) + -1/7^z + ...
sage: g*mu
1 + ...

sage: g = L([0], constant=1)
sage: F = L(None)
sage: F.define(1 + g*F)
sage: ff = [F[i] for i in range(1, 16)]; ff
[1, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 8, 1, 3, 3]
sage: oeis(ff)                              # optional, internet
0: A002033: Number of perfect partitions of n.
1: A074206: Kalmár's [Kalmar's] problem: number of ordered factorizations of n.
...