Race to replace Nakasone in full swing. Math gets complicated as Japan's contenders tally factions' support

Japan's prime ministerial sweepstakes are well under way, but it would be a bold man who could predict the outcome with confidence. Yasuhiro Nakasone's term expires on Oct. 31, and with four avowed candidates to succeed him, the ruling Liberal Democrats may well have to have a primary.

Almost all observers agree that whoever wins the prize, Mr. Nakasone's will be a hard act to follow. He has been prime minister for five years - the third longest tenure since World War II. He has established a reputation as a forceful voice in the councils of the Western nations - a position no previous Japanese statesman has enjoyed. He has forged close relationship with President Reagan, Britain's Prime Minister Margaret Thatcher, and France's President Francois Mitterrand.

Of the contenders (See accompanying story), Kiichi Miyazawa comes closest to Nakasone in international stature. But his reluctance to wheel and deal domestically keeps him from being the politician's politician.

Domestic politics are Noboru Takeshita's forte. But unless he shows more interest in international affairs and addresses the problem of Japan's huge foreign trade surplus, he may fall short of the 223 votes required to secure the LDP presidency.

Shintaro Abe seems to be everyone's second choice. A former journalist, he is nowhere near as cerebral as Mr. Miyazawa, but is pleasant and reasonably open.

Susumu Nikaido, in a way, is the spoiler. If he had not insisted on running, the influential faction controlled by former premier Kakuei Tanaka, would probably have united around Mr. Takeshita. But Mr. Nikaido insists his candidacy is for real - that he will manage to get enough votes from minor factions and nonaligned legislators to make him a viable contender. Nikaido attended college in the United States, and speaks comprehensible, if somewhat fractured English.

The arithmetics of the election are: The Liberal Democrats have 445 members in the two Diet (parliament) houses. A contender for the party presidency, which carries with it the prize of the prime ministership, must secure a simple majority, or 223 votes.

The conservative Liberal Democrats are divided into several factions. These are not so much policy-oriented bodies as groups to channel campaign funds to their members. The Takeshita faction has 113 members, the Miyazawa faction 89, the Nakasone faction 87, the Abe faction 85, the Komoto faction 32, and the Nikaido faction 14. Another 25 belong to no faction.

The contest is for a renewable two-year term as party president. If there are three contenders or less, a primary can be eliminated. But with Nikaido in the race, a primary seems inevitable. All party members as of July 31 are eligible to vote in the primary. Although nonbinding, a good primary turnout does have political implications: In 1978, Takeo Fukuda resigned the premiership when his rival won the primary. The breakup of the Tanaka faction strengthens Nakasone's ability to influence the choice of his successor. His faction's 87 votes figure prominently in each candidate's calculations.

Foreign policy will not be a major campaign issue. All factions support the Western alliance, security ties with the United States, and co-existence with Moscow to the extent that alliance security is not endangered.

So it all boils down to a question of nuances and implications. It will not be easy to maintain the proper balance between domestic and external considerations. But given the emotion-charged atmosphere of Japan's external relations today, any new premier will first have to convince his alliance partners that he is as concerned about global issues as his predecessor, Nakasone.

The four front-runners

Noboru Takeshita, secretary-general of the party and former finance minister. He was once considered former Premier Kakuei Tanaka's heir-apparent. But he incurred Mr. Tanaka's wrath when he attempted to form his own faction within the so-called Tanaka Army, largest of the party's major factions. Early this month, Takeshita formally set up his own faction, with 113 members. (All but 30 of the Tanaka faction members joined his group.) Takeshita is a whiz at organization and maneuvering, but seems the least internationally minded of the candidates.

Kiichi Miyazawa, incumbent finance minister. Fluent in English, an intellectual to his finger tips, Mr. Miyazawa enjoys an established reputation among international statesmen.

Shintaro Abe, head of the party's Executive Council and former foreign minister. Urbane, and well-connected, Mr. Abe has traveled extensively and developed a first-name relationship with US Secretary of State George Shultz.

Susumu Nikaido. Loyal to Mr. Tanaka, he heads 14 members formerly of this faction. Another 14 or 15 members are neutral. When Tanaka refused to acknowledge Takeshita as his successor, Nikaido secured the support of about half of the remainder.