A075059 a(n) = 1 + lcm(1, 2, ..., n) = 1 + A003418(n).

2, 2, 3, 7, 13, 61, 61, 421, 841, 2521, 2521, 27721, 27721, 360361, 360361, 360361, 720721, 12252241, 12252241, 232792561, 232792561, 232792561, 232792561, 5354228881, 5354228881, 26771144401, 26771144401, 80313433201, 80313433201

Offset: 0

Author

Amarnath Murthy, Sep 08 2002

Keywords

• nonn

Comments

Consider the triangle in which the n-th row contains the second run of n consecutive numbers such that the r-th term is divisible by r. Sequence gives the first column of the triangle. The first run trivially begins with 1.

Also the smallest of n consecutive integers (with the first greater than 1) divisible respectively by 1, 2, 3, ..., n. - Robert G. Wilson v, Oct 30 2014

Also the smallest number m > 1 such that m == 1 (mod i) for all 1 <= i <= n. - Franz Vrabec, Aug 18 2023

Examples

			First column of the triangle A075061:
   2;
   3,  4;
   7,  8,  9;
  13, 14, 15, 16;
  61, 62, 63, 64, 65;
  61, 62, 63, 64, 65, 66;
  ...
		

Crossrefs

Cf. A003418, A060401, A065500, A070198, A072562, A075061, A249051.

Programs

Magma

[Exponent(SymmetricGroup(n))+1 : n in [1..30]]; // Vincenzo Librandi, Oct 31 2014

Mathematica

Table[LCM@@Range[n] + 1, {n, 30}] (* Harvey P. Dale, Nov 15 2011 *)

PARI

a(n)=lcm([1..n])+1 \\ Charles R Greathouse IV, Nov 04 2014

Formula

a(n) = 1 + A003418(n).

Extensions

New definition from Vladeta Jovovic, Jun 16 2003

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar

a(0)=2 prepended by Max Alekseyev, Sep 04 2015