A075061 -id:A075061 - cp's OEIS frontend

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

Amarnath Murthy, Sep 08 2002

nonn

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

			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;
  ...

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

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

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

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

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

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

A060401 a(n) = minimal m such that m>n, n divides m, n-1 divides m-1, n-2 divides m-2 and so on down to 1 divides m-n+1.

Original entry on oeis.org

2, 4, 9, 16, 65, 66, 427, 848, 2529, 2530, 27731, 27732, 360373, 360374, 360375, 720736, 12252257, 12252258, 232792579, 232792580, 232792581, 232792582, 5354228903, 5354228904, 26771144425, 26771144426, 80313433227, 80313433228, 2329089562829, 2329089562830

Offset: 1

Christopher Burrows (cburrows(AT)math.upenn.edu), Apr 04 2001

nonn

A099427(a(n)) = n + 1. - Reinhard Zumkeller, Jul 02 2011

			a(5) = 65 because 5|65, 4|64, 3|63, 2|62, 1|61 and 65 is minimal.

Robert Israel, Table of n, a(n) for n = 1..2296

Rightmost diagonal of triangle in A075059. Cf. A075061, A075062.

Cf. A003418.

seq(n+ilcm($1..n),n=1..100); # Robert Israel, Jul 19 2016

a(n) = n + lcm(seq(i, i=1..n)).

a(n) = n + A003418(n). - Robert Israel, Jul 19 2016

A075062 Row sums of triangle in A075059.

Original entry on oeis.org

2, 7, 24, 58, 315, 381, 2968, 6756, 22725, 25255, 304986, 332718, 4684771, 5045145, 5405520, 11531656, 208288233, 220540491, 4423058830, 4655851410, 4888643991, 5121436573, 123147264516, 128501493420, 669278610325, 696049754751

Offset: 1

Amarnath Murthy, Sep 08 2002

nonn

For odd n, a(n) is a multiple of n.

Cf. A075059, A060401, A075061.

a(n)=n*A075059(n)+A000217(n-1). - R. J. Mathar, Mar 20 2007

More terms from R. J. Mathar, Mar 20 2007

cp's OEIS Frontend

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

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A060401 a(n) = minimal m such that m>n, n divides m, n-1 divides m-1, n-2 divides m-2 and so on down to 1 divides m-n+1.

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A075062 Row sums of triangle in A075059.

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