A275239 Highly composite numbers of class 1 (see comment).

3, 8, 16, 18, 30, 72, 144, 168, 252, 336, 420, 900, 960, 1008, 1080, 1440, 2160, 2880, 3360, 6300, 6720, 7920, 9240, 12600, 18480, 30240, 60480, 65520, 98280, 131040, 196560, 262080, 327600, 360360, 589680, 655200, 786240, 831600, 1108800, 1330560, 1663200

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, Jul 21 2016

Keywords

• nonn

Comments

Consider the sequence of highly composite numbers (HCN) (A002182). Let us say that its terms are HCN of class 0. Removing A002182 from the positive integers we obtain the sequence 3,5,7,8,9,10,11,13,14,15,16,17,18,...(1)

Consider the subsequence whose number of divisors set a record. We obtain 3,8,16,18,... We call this sequence HCN of class 1. It is A275239.

Furthermore, removing from sequence (1) the HCN of class 1 we obtain the sequence 5,7,9,10,11,13,14,15,17,19,20,21,... (2)

Again consider the subsequence whose number of divisors are records. We obtain 5,9,10,20,... We call this sequence HCN of class 2. It is A275240, etc.

Note that the sequence of HCN of class h>=1 numbers begins from Prime(h+1)(which is the unique prime in the sequence).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..78 (terms below 10^10)

Crossrefs

Cf. A002182, A275240, A275241, A275242, A275243, A275244.