A273379 -id:A273379 - cp's OEIS frontend

A273632 Numerator of ratio h/g, where h>g are smallest highly composite numbers such that interval (g, h) contains A273379(n).

2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 18, 18, 18, 3, 4, 3, 3, 4, 5, 6, 3, 3, 3, 6, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 4, 5, 3, 3, 3, 20, 17, 17, 6, 3, 3, 3, 3, 3, 6, 5, 4, 6, 5, 3, 3, 3, 3, 19, 3, 3, 3, 19, 3, 3, 3, 3, 3, 5, 4, 5, 3, 3, 4, 3, 3, 4, 3, 3, 3, 46, 46, 3

Offset: 1

Vladimir Shevelev, May 27 2016

Ratios begin 2,2,2,2,3/2,3/2,2,2,2,2,2,18/11,18/11,18/11,3/2,4/3,3/2,3/2,4/3,...

Denominators see in A273638.

Amiram Eldar, Table of n, a(n) for n = 1..7692

Cf. A002182, A273379.

a(22)-a(24) corrected and more terms added by Amiram Eldar, Sep 18 2019

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

Original entry on oeis.org

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

Offset: 1

David A. Corneth, May 22 2016

nonn

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).

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.

Cf. A067128, A273379.

cp's OEIS Frontend

A273632 Numerator of ratio h/g, where h>g are smallest highly composite numbers such that interval (g, h) contains A273379(n).

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