A333665 Numbers that occur in A057144 arranged in ascending order.

1, 2, 4, 6, 12, 24, 36, 60, 120, 240, 360, 720, 840, 1680, 2520, 5040, 10080, 27720, 30240, 55440, 110880, 166320, 332640, 720720, 1441440, 2162160, 3603600, 4324320

Offset

1,2

Comments

30240 is the smallest term that is not highly composite (A002182).

From Hal M. Switkay, Jul 25 2022: (Start)

It appears that each term is the least number having its prime signature (A025487).

Although it would be desirable to produce more terms of this sequence, the first 28 terms represent the union of at least the first 20000 terms of A057144.

The smallest of the most frequently occurring numbers in the 1-to-k multiplication table, A057144(k), do not constitute a nondecreasing function of k. Thus the minimal values of k corresponding to terms of this sequence do not form an increasing sequence. For example, A057144(k) = 60 when 20 <= k <= 23 or 30 <= k <= 39; but A057144(k) = 24 when 24 <= k <= 29, and A057144(k) = 36 when 18 <= k <= 19. (End)

Links

Table of n, a(n) for n=1..28.

Benjamin Dickman, What number appears most often in a n X n multiplication table?, Mathematics StackExchange, May 2014.

Example

For 6 <= k <= 11, the smallest of the most frequently occurring numbers in the 1-to-k multiplication table is 6. a(4) = 6, because it is the fourth natural number to be the smallest of the most frequently occurring numbers in the 1-to-k multiplication table. - Hal M. Switkay, Jul 27 2022

Crossrefs

Cf. A002182, A057144.

Sequence in context: A362782 A365900 A365681 * A355595 A050293 A330744

Adjacent sequences: A333662 A333663 A333664 * A333666 A333667 A333668

Keyword

nonn,more

Author

Dmitry Kamenetsky, Sep 03 2020

Extensions

a(20)-a(28) from Hal M. Switkay, using the b-file of A057144, Jul 25 2022

Status

approved