A117583 - OEIS

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A117583

The number of ratios t/(t-1), where t is a triangular number, which factor into primes less than or equal to prime(n).

0, 1, 3, 7, 9, 16, 22, 29, 35, 39, 50, 57, 68, 84, 100, 112, 127, 151, 167

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

As in the case of square numerators, triangular numerators of superparticular ratios m/(m-1) factorizable only up to a relatively small prime p are relatively common.

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

LINKS

Table of n, a(n) for n=1..19.

Lucas A. Brown, stormer.py.

E. F. Ecklund and R. B. Eggleton, Prime factors of consecutive integers, Amer. Math. Monthly, 79 (1972), 1082-1089.

D. H. Lehmer, On a problem of Størmer, Ill. J. Math., 8 (1964), 57-79.

Wikipedia, Størmer's theorem

EXAMPLE

The ratios counted by a(3) are 3/2, 6/5, and 10/9.

The ratios counted by a(4) are 3/2, 6/5, 10/9, 15/14, 21/20, 28/27, and 36/35.

CROSSREFS

Cf. A002071, A117582.