Arkhemakhus is the son of Herakles and Patro who is one of the daughters of King Thespius. During his stay in the court of King Thespius, Herakles impregnated 49 of the 50 daughters of Thespius. Among them was Patro who Herakles would lay with one night. The result of that particular encounter was Arkhemakhus.
"by Patro he [Herakles] had Arkhemakhus"
- Apollod. Biblioteca, 2.7.8