A273415 The smallest term of A273379 having n primes between two consecutive prime divisors.

10, 4680, 6585701522400, 193394747145600, 27377180785991836800, 29378941900252048776672000, 5384823686347760468943298225056000, 404593694258692410380118300618528000, 1714431214566179268370439406441900195214656000, 180656647480221782329653424360823828484237888000

Offset: 1

Author

David A. Corneth, May 22 2016

Keywords

• nonn

Comments

Is this sequence infinite?

In the prime factorization of a(n), the 'gap' occurs before the largest prime divisor. For example, 4680 has distinct prime divisors 2, 3, 5 and 13. The gap is before the largest prime 13. All primes up to and including the second largest prime are a divisor of a(n).

Links

• P. Erdős, On Highly composite numbers, J. London Math. Soc. 19 (1944), 130--133 MR7,145d; Zentralblatt 61,79.
• Vladimir Shevelev, On Erdős constant, arXiv:1605.08884 [math.NT], 2016.

Crossrefs

Cf. A067128, A273379.