A365059 a(1) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of A008472(a(n-1)), the sum of the distinct primes dividing a(n-1).

2, 4, 6, 5, 10, 7, 14, 9, 3, 12, 15, 8, 16, 18, 20, 21, 30, 40, 28, 27, 24, 25, 35, 36, 45, 32, 22, 13, 26, 60, 50, 42, 48, 55, 64, 34, 19, 38, 63, 70, 56, 54, 65, 72, 75, 80, 49, 77, 90, 100, 84, 96, 85, 44, 39, 112, 81, 33, 98, 99, 126, 108, 95, 120, 110, 144, 105, 135, 88, 52, 150, 130, 140

Offset: 1

Author

Scott R. Shannon, Aug 19 2023

Keywords

• nonn

Comments

In the first 500000 terms the only fixed points are 38 and 209, although it is likely more exist. In the same range the smallest missing numbers are 311, 313, 337. The sequence is conjectured to be a permutation of the integers >= 2.

Examples

			a(3) = 6 as a(2) = 4 and A008472(4) = 2, and 6 is the smallest unused number that is a multiple of 2.
a(11) = 15 as a(10) = 12 and A008472(12) = 5, and 15 is the smallest unused number that is a multiple of 5.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 500000 terms. The green line is a(n) = n.

Crossrefs

Cf. A008472, A365060, A300813.