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

1,3

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.

Sequence in context: A057463 A287124 A118258 * A126106 A064194 A036978

Adjacent sequences: A117580 A117581 A117582 * A117584 A117585 A117586

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