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Claim. The number $1$ is a sum of reciprocals of $101$ distinct integers, each the product of exactly two distinct primes: the article prints the denominators, from $6,10,14,15,21,\ldots$ to $578261,699481,1838171$, and says they were found with a pocket calculator. This is the instance $a/b=1$ of Problem 306, answered yes, and the first such representation on record; the article asks what the shortest one is. Exact rational arithmetic for this corpus confirms that the $101$ printed numbers are distinct products of two distinct primes and that their 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 length question, which Johnson (48 terms, 1978) and Watanabe (47 terms, 2020) later improved on.

Origin. The article reaches the representation from the arithmetic derivative: an integer $n$ with $D(D(n))=n\ne D(n)$ would give $1=(\sum_i1/p_i)(\sum_j1/q_j)$ for two sets of distinct primes, the question of Problem 307, which the author writes he cannot decide, and such a product would in particular write $1$ as a sum of reciprocals of two-prime integers. The article also reports, from a letter of Graham, that Erdős and Graham had shown every $p/q$ with $q$ squarefree to be a sum of reciprocals of squarefree integers with exactly $k$ distinct prime factors for every $k\ge3$, with "many cases" for $k=2$, unpublished; the 1980 monograph records the same remark, and the site's question is its two-prime case.

Standing. Claimed. Barbeau, E. J., Expressing one as a sum of distinct reciprocals: comments and a bibliography, Eureka (Ottawa) 3 (1977), no. 7 (August--September 1977), 178--181; the journal became Crux Mathematicorum in 1978, and the issue is 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. Eureka was a problem-solving journal of the Carleton-Ottawa Mathematics Association, and no evidence that the article was refereed is recorded, so refereed is not listed. The site's commentary credits the article with the first representation of $1$ on a problem it labels OPEN, which is not acceptance of a claim, so reviewed is not listed. The example is reproduced, by count and date, in Watanabe's preprint (p. 2) and the 1980 monograph (p. 38).