A323890 a(1) = 1, a(2) = 2; thereafter a(n+1) = smallest unused divisor of a(n) if there are any, otherwise a(n) + a(n-1).

1, 2, 3, 5, 8, 4, 12, 6, 18, 9, 27, 36, 63, 7, 70, 10, 80, 16, 96, 24, 120, 15, 135, 45, 180, 20, 200, 25, 225, 75, 300, 30, 330, 11, 341, 31, 372, 62, 434, 14, 448, 28, 476, 17, 493, 29, 522, 58, 580, 116, 696, 87, 783, 261, 1044, 174, 1218, 21, 1239, 59, 1298, 22, 1320, 33, 1353

Offset: 1

Author

Ivan Neretin, Sep 02 2019

Keywords

• nonn
• look

Examples

			a(6) = 4, and all divisors of 4 are already used, hence a(7) = a(6) + a(5) = 8 + 4 = 12. Now the smallest unused divisor of 12 is 6, hence a(8) = 6.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A050196, A085947.

Programs

Mathematica

Nest[Append[#, If[(d = Complement[Divisors@#[[-1]], #]) == {}, #[[-1]] + #[[-2]], Min[d]]] &, {1, 2}, 63]