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

Offset: 1

Author

Gene Ward Smith, Apr 02 2006

Keywords

• nonn
• hard
• more

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

Examples

			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.
		

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

Crossrefs

Cf. A002071, A117582.

Extensions

a(14)-a(18) by Lucas A. Brown, Oct 04 2022

a(19) from Lucas A. Brown, Oct 16 2022