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%I #27 Apr 06 2020 03:15:06
%S 3,8,16,18,30,72,144,168,252,336,420,900,960,1008,1080,1440,2160,2880,
%T 3360,6300,6720,7920,9240,12600,18480,30240,60480,65520,98280,131040,
%U 196560,262080,327600,360360,589680,655200,786240,831600,1108800,1330560,1663200
%N Highly composite numbers of class 1 (see comment).
%C 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)
%C 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.
%C 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)
%C 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.
%C Note that the sequence of HCN of class h>=1 numbers begins from Prime(h+1)(which is the unique prime in the sequence).
%H Amiram Eldar, <a href="/A275239/b275239.txt">Table of n, a(n) for n = 1..78</a> (terms below 10^10)
%Y Cf. A002182, A275240, A275241, A275242, A275243, A275244.
%K nonn
%O 1,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Jul 21 2016
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