cp's OEIS Frontend

By a theorem of Størmer, the number of such integers is finite; moreover he provides an algorithm for finding the complete list.

Størmer came to this problem from music theory. Another way to formulate the statement of the theorem is that for any prime p, there are only a finite number of superparticular ratios R = n/(n-1) such that R factors into primes less than or equal to p. The numerator of the smallest such R for the i-th prime is the i-th element of the above sequence. For instance, 81/80, the syntonic comma, is the smallest 5-limit superparticular "comma", i.e., small ratio greater than one.

An effective abc conjecture (c < rad(abc)^2) would imply that a(21) = 2286831727304145 and a(22) = ... = a(26) = 9591468737351909376 and a(27) = ... = a(32) = 19316158377073923834001 and a(33) = 124225935845233319439174. - Lucas A. Brown, Oct 16 2022

By a theorem of Størmer, the number of ratios m/(m-1) factoring into primes only up to p is finite. Some of these have square numerators.

Equivalently, a(n) is the number of triples of consecutive prime(n)-smooth numbers. - Lucas A. Brown, Oct 04 2022