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
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
KEYWORD
nonn,hard,more
AUTHOR
Gene Ward Smith, Apr 02 2006
EXTENSIONS
a(14)-a(18) by Lucas A. Brown, Oct 04 2022
a(19) from Lucas A. Brown, Oct 16 2022
STATUS
approved