OFFSET
1,1
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, Jul 21 2016
STATUS
approved