

A117582


The number of ratios t/(t1), where t is a square number, which factor into primes less than or equal to prime(n).


2



0, 2, 5, 10, 15, 24, 34, 46, 57, 74, 90, 114, 141, 174, 208, 244, 287, 334, 387
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OFFSET

1,2


COMMENTS

By a theorem of Størmer, the number of ratios m/(m1) 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


LINKS



EXAMPLE

The ratios counted by a(3) are 4/3, 9/8, 16/15, 25/24, and 81/80.
The ratios counted by a(4) are 4/3, 9/8, 16/15, 25/24, 36/35, 49/48, 64/63, 81/80, 225/224, and 2401/2400.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



EXTENSIONS



STATUS

approved



