It is frequently written that the Japanese are distrustful of foreigners. The other side of that coin is that they admire their countrymen who are able to deal with those foreigners, and this is probably the main reason that sometime this spring or summer Prime Minister Takeo Fukuda will visit President Carter in Washington.

By all accounts, there are no burning issues to be discussed between them. It is assumed here that the trip has more to do with Fukuda's political requirements than anything else. He is being blamed in Japan for the persistent recession, and his declining prestige is measured by monthly polls. Like other world leaders, including Carter, Japanese Prime Minister think that foreign travel is good politics and believe that a few hours on the world stage helps them at home.

There is a special reason in the case of Japan. Ever since the United States helped this country on the road to post-war recovery, it has been important for a prime minister to show he has a good friend in Washington. To demonstrate that he is the man in charge, he must show he can deal with Americans. "It is extremely important for a prime minister to show that he can manage the relationship with Washington," one diplomat said recently.

As a result, the trek to the United States has become almost an annual ritual. The incumbent prime minister of Japan has attended a U.S. summit meeting in each of the past six years (only one of them in Tokyo) and has missed in only three years since 1965.

When the visit this year gets down to specifics, the Japanese are expected to want to talk about military security and economics. A year ago, the news of an impending withdrawal of U.S. ground forces from South Korea hit Japan hard. Months of subsequent reassurances that the U.S. guarantees Japan's security have eased the shock but not elimated it. Fukuda will be looking for some reassurances on old security pledges this time.

The economic issue is more pressing. American and Japan have just gone through some bitter times in trade negotiations. For nearly three months, Tokyo newspapers were full of stories about American demands to get rid of Japan's trade surplus and American threats of protectionism against Japanese products. The Japanese don't like direct confrontations much and the United States, in the person of Special Trade Representative Robert Strauss, presented one in unmistakable terms.

The barrage of demands, persisting over such a long time, left the Japanese feelings "concerned ," a prominent social scientist abserved recently. A popular new commentor, Hisanori Isomura, also said that the unpleasant episode underscored Japan's "goat-ability" - its habit of being made a scapegoat for world problems. So Fukuda will want some well-publicized reassurances that the hatchet has now been buried.

For Fukuda, the Washington trip this year will be one of three major foreign appearances. He will represent Japan at the economic summit meeting in Bonn in July and expect to appear at the United Nations for a speech on the disarmament in May. It is an unusually busy year abroad for a Japanese Prime minister and reflects a growing sentiment among many Japanese - a sentiment encouraged by Americans - that their country should be more assertive in world affairs.

Whether it all adds up to a political gain for Fukuda will be determined late this year by his political fortunes. It is widely believed that he wants to dissolve the Parliament and hold new elections at an opportune time when he is riding a sucess wave from his foreign ventures.

If the economy fails to revive this year, he is likely to face a strong challenge from his chief rival, Massayoshi Ohira, secretary general of the ruling Liberal-Democratic Party. Fukuda's foreign travels, including the meeting with Carter are being planned with one eye on Ohira.

Just as in the United States, no one in Japan really knows whether an act on a world stage has much bearing on domestic politics. It may be that the Japanese really don't pay much attention to what their Prime Minister does abroad, the important thing is that politicians believe they pay a lot of attention and they act on that premise.