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Claim. The number $1$ is a sum of the reciprocals of the $48$ integers

$$6,10,14,15,21,22,26,33,34,35,38,39,46,51,55,57,58,62,65,69,77,82,85,86,87,91,93,95,115,119,123,133,155,187,203,209,215,221,247,265,287,299,319,323,391,689,731,901,$$

each the product of two distinct primes. This is the instance $a/b=1$ of Problem 306, answered yes, with fewer terms than Barbeau's $101$ (his claim page); the letter reports that at least $38$ terms are needed and that sets of $50$ were known. Exact rational arithmetic for this corpus confirms that the $48$ numbers are distinct products of two distinct primes whose reciprocals sum to exactly $1$, an author-recorded check and not a review.

Covers. The instance $a/b=1$ only. Not covered: any other rational, and the least number of terms, which Watanabe (47 terms, 2020) lowered by one.

Standing. Claimed. Johnson, A. W., Jr., Letter to the editor, Crux Mathematicorum 4 (1978), no. 7 (August--September 1978), 190, in the Canadian Mathematical Society's archive at the link above; the issue gives no day, and the day in this page's name is the first of the issue's first month. A letter in a problem-solving journal carries no evidence of refereeing, so refereed is not listed, although the denominators are reproduced in the refereed paper of Butler, Erdős and Graham (Integers 15 (2015), p. 2) and in Watanabe's preprint (p. 2), and the site's discussion reports that OEIS A201650 lists them. The site's commentary does not name the letter, and the problem is labeled OPEN, so reviewed is not listed.