Question: For which dynasty did the father of Pareherwenemef serve as Pharaoh?

Context paragraphs:
Vizier (Ancient Egypt): The vizier ( or ) was the highest official in Ancient Egypt to serve the pharaoh (king) during the Old, Middle, and New Kingdoms. Vizier is the generally accepted rendering of ancient Egyptian "tjati", "tjaty" etc., among Egyptologists.  The "Instruction of Rekhmire" ("Installation of the Vizier"), a New Kingdom text, defines many of the duties of the "tjaty", and lays down codes of behavior.  The viziers were often appointed by the pharaoh.  During the 4th Dynasty and early 5th Dynasty, viziers were exclusively drawn from the royal family; from the period around the reign of Neferirkare Kakai onwards, they were chosen according to loyalty and talent or inherited the position from their fathers.

Pepi III: Seneferankhre Pepi III may have been a pharaoh of the Sixteenth dynasty of Egypt during the Second Intermediate Period.  According to Wolfgang Helck he was the fifth pharaoh of the dynasty.  Alternatively, according to Jürgen von Beckerath, he was the thirteenth pharaoh of the dynasty.  Because his position in the 16th dynasty is highly uncertain, it is not clear who were his predecessor and successor.

Ahmose I: Ahmose I (Egyptian: Jˁḥ ms(j.w), sometimes written "Amosis I", "Amenes" and "Aahmes" and meaning "Born of Iah") was a pharaoh of ancient Egypt and the founder of the Eighteenth dynasty.  He was a member of the Theban royal house, the son of pharaoh Seqenenre Tao and brother of the last pharaoh of the Seventeenth dynasty, King Kamose.  During the reign of his father or grandfather, Thebes rebelled against the Hyksos, the rulers of Lower Egypt.  When he was seven years old his father was killed, and he was about ten when his brother died of unknown causes, after reigning only three years.  Ahmose I assumed the throne after the death of his brother, and upon coronation became known as Neb-Pehty-Re ("The Lord of Strength is Re").  The name "Ahmose" is a combination of the divine name 'Ah' (see Iah) and the combining form '-mose'.

Pareherwenemef (20th dynasty): Pareherwenemef (“Re is with his left arm”) was an ancient Egyptian prince of the 20th dynasty, a son of pharaoh Ramesses III.  Just like several of his brothers, he was named after a son of Ramesses II, whom Ramesses III tried to emulate (see Pareherwenemef).  He is depicted in his father's mortuary temple at Medinet Habu.  Both he and his brother Khaemwaset are called firstborn sons of the king; they were possibly the firstborns of different wives.  He was buried in QV42.

Ramesses III: Usimare Ramesses III (also written Ramses and Rameses) was the second Pharaoh of the Twentieth Dynasty and is considered to be the last monarch of the New Kingdom to wield any substantial authority over Egypt.  His long reign saw the decline of Egyptian political and economic power, linked to a series of invasions and internal economic problems.

Pareherwenemef: Pareherwenemef (Pre-hir-wonmef, Prehirwenemef, Rehirwenemef ) was an ancient Egyptian prince of the 19th dynasty, the third son of Pharaoh Ramesses II, the second by Queen Nefertari.

Twenty-seventh Dynasty of Egypt: The Twenty-seventh Dynasty of Egypt (notated Dynasty XXVII, alternatively 27th Dynasty or Dynasty 27), also known as the First Egyptian Satrapy (Old Persian: Mudrāya ) was effectively a province (satrapy) of the Achaemenid Persian Empire between 525 BC to 404 BC.  It was founded by Cambyses II, the King of Persia, after his conquest of Egypt and subsequent crowning as Pharaoh of Egypt, and was disestablished upon the rebellion and crowning of Amyrtaeus as Pharaoh.

Djedkheperew: Djedkheperew (also known as Djedkheperu) was an Egyptian pharaoh of the 13th Dynasty reigning for an estimated two-year period, from c. 1772 BC until 1770 BC.  According to Egyptologists Kim Ryholt and Darrell Baker, Djedkheperew was the 17th king of this dynasty.  Djedkheperew is this pharaoh's Horus name; the prenomen and nomen of Djedkheperew, which would normally be employed by modern conventions to name a pharaoh, are unknown.

Min festival: The Min festival was an ancient Egyptian ceremony which was held to celebrate the continued rule of a pharaoh.  It dates back to Predynastic Egypt and was still very popular during the 19th dynasty reign of Pharaoh Ramesses II.  The festival was connected with the worship of the king and was held in the last month of the summer.  It was carried out by the king himself, followed by his wife, royal family, and the court.  When the king entered the sanctuary of the deity Min, he brought offerings and burning incense.  Then, the standing god was carried out of the temple on a shield carried by 22 priests.  In front of the statue of the god there were also two small seated statues of the pharaoh.  In front of the god Min there was a large ceremonial procession that included dancers and priests.  In front of them was a king with a white bull that was wearing a solar disc between its horns.  When the god arrived at the end of the procession, he was given sacrificial offerings from the pharaoh.  At the end of the festival, the pharaoh was given a bundle of cereal that symbolised fertility.

Khaankhre Sobekhotep: Khaankhre Sobekhotep (now believed to be Sobekhotep II; known as Sobekhotep I in older studies) was an pharaoh of the Thirteenth Dynasty of Egypt during the Second Intermediate Period.  According to egyptologists Kim Ryholt and Darrell Baker, Khaankhre Sobekhotep was the 13th pharaoh of the dynasty and had a short reign ca. 1735 BC.  Alternatively, Jürgen von Beckerath sees him as the 16th pharaoh of the dynasty.

Supporting paragraphs: Pareherwenemef (20th dynasty) Ramesses III
Answer: Twentieth Dynasty