OFFSET
1,2
COMMENTS
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
LINKS
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 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
Gene Ward Smith, Apr 02 2006
EXTENSIONS
Offset 1 and a(14)-a(18) by Lucas A. Brown, Oct 04 2022
a(19) from Lucas A. Brown, Oct 16 2022
STATUS
approved