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

0,1

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

Links

Table of n, a(n) for n=0..28.

Formula

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

Example

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;
  ...

Mathematica

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

Prog

(Magma) [Exponent(SymmetricGroup(n))+1 : n in [1..30]]; // Vincenzo Librandi, Oct 31 2014
(PARI) a(n)=lcm([1..n])+1 \\ Charles R Greathouse IV, Nov 04 2014

Crossrefs

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

Sequence in context: A184841 A109277 A093437 * A060357 A064714 A152255

Adjacent sequences: A075056 A075057 A075058 * A075060 A075061 A075062

Keyword

nonn

Author

Amarnath Murthy, Sep 08 2002

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

Status

approved