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

1,2

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A133058.

Sequence in context: A244000 A201937 A211456 * A196205 A196141 A082210

Adjacent sequences: A309662 A309663 A309664 * A309666 A309667 A309668

Keyword

nonn,look

Author

Dennis Reichard, Aug 11 2019

Status

approved