Let t>1 be a rational number. Is ∑_n=1^∞frac1t^n-1=∑_n=1^∞ fractau(n)t^n irrational, where tau(n) counts the divisors of n?

Erdős Problem #1049 — Let $t>1$ be a rational number. Is $\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}$ irrational, where $\tau(n)$ counts the divisors of $n$ ?

About 38 years old · traced to 1988

Let $t>1$ be a rational number. Is $\sum_{n=1}^\infty\frac{1}{t^n-1}=\sum_{n=1}^\infty \frac{\tau(n)}{t^n}$ irrational, where $\tau(n)$ counts the divisors of $n$ ?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

irrationality

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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