# Closed form for $\sum_{n=1}^\infty \frac{1}{P(n)}$, where $P(n)$ is the partition function.

Is there a closed form for the following infinite series? $$\sum_{n=1}^\infty \frac{1}{P(n)}=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{5}+...$$ where $P(n)$ is the partition function.

• Interesting question. Does it come from some applications? Inverse symbolic calculator does not propose anything promising. – Start wearing purple Sep 11 '15 at 15:06
• To be more precise, with $20$ digits ISC says "Wow, really found nothing". – Start wearing purple Sep 11 '15 at 15:30
• See OEIS A$078506$. – Lucian Sep 11 '15 at 22:51