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.

1, 2, 3, 6, 10, 12, 14, 15, 18, 4, 20, 30, 21, 42, 60, 66, 22, 24, 70, 78, 84, 90, 26, 28, 33, 34, 35, 36, 102, 105, 5, 38, 110, 39, 7, 210, 114, 120, 126, 330, 390, 420, 130, 132, 138, 140, 462, 510, 150, 546, 570, 154, 40, 44, 45, 156, 8, 165, 630, 660, 168, 170, 174, 9, 46, 48, 690

Offset: 1

Author

Scott R. Shannon, Jul 12 2023

Keywords

• nonn

Comments

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.

Examples

			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.
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.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000.

Crossrefs

Cf. A001221, A363162, A355702, A355647, A355649, A352867.