A309665 a(1)=1; for n > 1, a(n) = a(n-1)/gcd(a(n-1),n) + n + 1.

1, 4, 8, 7, 13, 20, 28, 16, 26, 24, 36, 16, 30, 30, 18, 26, 44, 41, 61, 82, 104, 75, 99, 58, 84, 69, 51, 80, 110, 42, 74, 70, 104, 87, 123, 78, 116, 97, 137, 178, 220, 153, 197, 242, 288, 191, 239, 288, 338, 220, 272, 121, 175, 230, 102, 108, 94, 106, 166

Offset: 1

Author

Dennis Reichard, Aug 11 2019

Keywords

• nonn
• look

Comments

n is a lower bound on a(n), furthermore n+3 is a lower bound if n > 2. This can easily be proved by induction. It appears that both the average value and the upper bound grow either linearly or slightly faster than linearly.

Examples

			a(4) = a(3)/gcd(a(3),4) + 4 + 1 = 8/gcd(8,4) + 5 = 8/4 + 5 = 2 + 5 = 7.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A133058.

Programs

Magma

[n le 1 select 1 else  Self(n-1)/Gcd(Floor(Self(n-1)),n) + n + 1 : n in [1..60]]; // Marius A. Burtea, Aug 11 2019

Mathematica

a[1] = 1; a[n_] := a[n] = a[n-1]/GCD[a[n - 1], n] + n + 1; Array[a, 60] (* Amiram Eldar, Aug 14 2019 *)