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A364164 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of distinct prime factors as the sum of all previous terms.

%I A364164 #10 Jul 12 2023 11:05:50
%S A364164 1,2,3,6,10,12,14,15,18,4,20,30,21,42,60,66,22,24,70,78,84,90,26,28,
%T A364164 33,34,35,36,102,105,5,38,110,39,7,210,114,120,126,330,390,420,130,
%U A364164 132,138,140,462,510,150,546,570,154,40,44,45,156,8,165,630,660,168,170,174,9,46,48,690
%N A364164 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of distinct prime factors as the sum of all previous terms.
%C A364164 In the first 20000 terms the largest value is a(14889) = 15825810 which contains eight distinct prime factors. In the same range there are 593 terms that are prime, the last being a(19985) = 4339, while the smallest number not to appear is 4349. It is likely all numbers eventually appear.
%H A364164 Scott R. Shannon, <a href="/A364164/b364164.txt">Table of n, a(n) for n = 1..10000</a>.
%e A364164 a(3) = 3 as the sum of all previous terms is 1 + 2 = 3 which contains one distinct prime factor, and 3 is the smallest unused number that also contains one distinct prime factor.
%e A364164 a(6) = 12 as the sum of all previous terms is 1 + 2 + 3 + 6 + 10 = 22 which contains two distinct prime factors, and 12 is the smallest unused number that also contains two distinct prime factors.
%Y A364164 Cf. A001221, A363162, A355702, A355647, A355649, A352867.
%K A364164 nonn
%O A364164 1,2
%A A364164 _Scott R. Shannon_, Jul 12 2023