Erdős Problem #414 — Let $h_1(n)=h(n)=n+\tau(n)$ (where $\tau(n)$ counts the number of divisors of $n$ ) and $h_k(n)=h(h_{k-1}(n))$ . Is it true, for any $m,n$ , there exist $i$ and $j$ such that $h_i(m)=h_j(n)$ ?

About 46 years old · traced to 1980

Let $h_1(n)=h(n)=n+\tau(n)$ (where $\tau(n)$ counts the number of divisors of $n$ ) and $h_k(n)=h(h_{k-1}(n))$ . Is it true, for any $m,n$ , there exist $i$ and $j$ such that $h_i(m)=h_j(n)$ ?

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.

iterated-functions number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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